Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Question
Chapter 8.1, Problem 22PS
To determine
To find: The limit of given sequence
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4
6. Consider the sequence defined recursively by
2
an+1 = 1/(a₁ + ²)
an
2
If ao = 1, does the sequence converge? If so, what is the limit?
2.
Show that the sequence in Q1(a) is eventually strictly decreasing by calculating
an+1 - an. Also show that {an} is bounded below. What can you conclude about the
2n² + 1
sequence?
for an
n²-2
=
Q1. Let an = (-1)"an-1+ 2an-2, ao = 1 and a = 2. Determine the following
terms of the sequence given by the above recurrence relation.
(i) a2
(ii) az
Chapter 8 Solutions
Calculus
Ch. 8.1 - Prob. 1PSCh. 8.1 - Prob. 2PSCh. 8.1 - Prob. 3PSCh. 8.1 - Prob. 4PSCh. 8.1 - Prob. 5PSCh. 8.1 - Prob. 6PSCh. 8.1 - Prob. 7PSCh. 8.1 - Prob. 8PSCh. 8.1 - Prob. 9PSCh. 8.1 - Prob. 10PS
Ch. 8.1 - Prob. 11PSCh. 8.1 - Prob. 12PSCh. 8.1 - Prob. 13PSCh. 8.1 - Prob. 14PSCh. 8.1 - Prob. 15PSCh. 8.1 - Prob. 16PSCh. 8.1 - Prob. 17PSCh. 8.1 - Prob. 18PSCh. 8.1 - Prob. 19PSCh. 8.1 - Prob. 20PSCh. 8.1 - Prob. 21PSCh. 8.1 - Prob. 22PSCh. 8.1 - Prob. 23PSCh. 8.1 - Prob. 24PSCh. 8.1 - Prob. 25PSCh. 8.1 - Prob. 26PSCh. 8.1 - Prob. 27PSCh. 8.1 - Prob. 28PSCh. 8.1 - Prob. 29PSCh. 8.1 - Prob. 30PSCh. 8.1 - Prob. 31PSCh. 8.1 - Prob. 32PSCh. 8.1 - Prob. 33PSCh. 8.1 - Prob. 34PSCh. 8.1 - Prob. 35PSCh. 8.1 - Prob. 36PSCh. 8.1 - Prob. 37PSCh. 8.1 - Prob. 38PSCh. 8.1 - Prob. 39PSCh. 8.1 - Prob. 40PSCh. 8.1 - Prob. 41PSCh. 8.1 - Prob. 42PSCh. 8.1 - Prob. 43PSCh. 8.1 - Prob. 44PSCh. 8.1 - Prob. 45PSCh. 8.1 - Prob. 46PSCh. 8.1 - Prob. 47PSCh. 8.1 - Prob. 48PSCh. 8.1 - Prob. 49PSCh. 8.1 - Prob. 50PSCh. 8.1 - Prob. 51PSCh. 8.1 - Prob. 52PSCh. 8.1 - Prob. 53PSCh. 8.1 - Prob. 54PSCh. 8.1 - Prob. 55PSCh. 8.1 - Prob. 56PSCh. 8.1 - Prob. 57PSCh. 8.1 - Prob. 58PSCh. 8.1 - Prob. 59PSCh. 8.1 - Prob. 60PSCh. 8.2 - Prob. 1PSCh. 8.2 - Prob. 2PSCh. 8.2 - Prob. 3PSCh. 8.2 - Prob. 4PSCh. 8.2 - Prob. 5PSCh. 8.2 - Prob. 6PSCh. 8.2 - Prob. 7PSCh. 8.2 - Prob. 8PSCh. 8.2 - Prob. 9PSCh. 8.2 - Prob. 10PSCh. 8.2 - Prob. 11PSCh. 8.2 - Prob. 12PSCh. 8.2 - Prob. 13PSCh. 8.2 - Prob. 14PSCh. 8.2 - Prob. 15PSCh. 8.2 - Prob. 16PSCh. 8.2 - Prob. 17PSCh. 8.2 - Prob. 18PSCh. 8.2 - Prob. 19PSCh. 8.2 - Prob. 20PSCh. 8.2 - Prob. 21PSCh. 8.2 - Prob. 22PSCh. 8.2 - Prob. 23PSCh. 8.2 - Prob. 24PSCh. 8.2 - Prob. 25PSCh. 8.2 - Prob. 26PSCh. 8.2 - Prob. 27PSCh. 8.2 - Prob. 28PSCh. 8.2 - Prob. 29PSCh. 8.2 - Prob. 30PSCh. 8.2 - Prob. 31PSCh. 8.2 - Prob. 32PSCh. 8.2 - Prob. 33PSCh. 8.2 - Prob. 34PSCh. 8.2 - Prob. 35PSCh. 8.2 - Prob. 36PSCh. 8.2 - Prob. 37PSCh. 8.2 - Prob. 38PSCh. 8.2 - Prob. 39PSCh. 8.2 - Prob. 40PSCh. 8.2 - Prob. 41PSCh. 8.2 - Prob. 42PSCh. 8.2 - Prob. 43PSCh. 8.2 - Prob. 44PSCh. 8.2 - Prob. 45PSCh. 8.2 - Prob. 46PSCh. 8.2 - Prob. 47PSCh. 8.2 - Prob. 48PSCh. 8.2 - Prob. 49PSCh. 8.2 - Prob. 50PSCh. 8.2 - Prob. 51PSCh. 8.2 - Prob. 52PSCh. 8.2 - Prob. 53PSCh. 8.2 - Prob. 54PSCh. 8.2 - Prob. 55PSCh. 8.2 - Prob. 56PSCh. 8.2 - Prob. 57PSCh. 8.2 - Prob. 58PSCh. 8.2 - Prob. 59PSCh. 8.2 - Prob. 60PSCh. 8.3 - Prob. 1PSCh. 8.3 - Prob. 2PSCh. 8.3 - Prob. 3PSCh. 8.3 - Prob. 4PSCh. 8.3 - Prob. 5PSCh. 8.3 - Prob. 6PSCh. 8.3 - Prob. 7PSCh. 8.3 - Prob. 8PSCh. 8.3 - Prob. 9PSCh. 8.3 - Prob. 10PSCh. 8.3 - Prob. 11PSCh. 8.3 - Prob. 12PSCh. 8.3 - Prob. 13PSCh. 8.3 - Prob. 14PSCh. 8.3 - Prob. 15PSCh. 8.3 - Prob. 16PSCh. 8.3 - Prob. 17PSCh. 8.3 - Prob. 18PSCh. 8.3 - Prob. 19PSCh. 8.3 - Prob. 20PSCh. 8.3 - Prob. 21PSCh. 8.3 - Prob. 22PSCh. 8.3 - Prob. 23PSCh. 8.3 - Prob. 24PSCh. 8.3 - Prob. 25PSCh. 8.3 - Prob. 26PSCh. 8.3 - Prob. 27PSCh. 8.3 - Prob. 28PSCh. 8.3 - Prob. 29PSCh. 8.3 - Prob. 30PSCh. 8.3 - Prob. 31PSCh. 8.3 - Prob. 32PSCh. 8.3 - Prob. 33PSCh. 8.3 - Prob. 34PSCh. 8.3 - Prob. 35PSCh. 8.3 - Prob. 36PSCh. 8.3 - Prob. 37PSCh. 8.3 - Prob. 38PSCh. 8.3 - Prob. 39PSCh. 8.3 - Prob. 40PSCh. 8.3 - Prob. 41PSCh. 8.3 - Prob. 42PSCh. 8.3 - Prob. 43PSCh. 8.3 - Prob. 44PSCh. 8.3 - Prob. 45PSCh. 8.3 - Prob. 46PSCh. 8.3 - Prob. 47PSCh. 8.3 - Prob. 48PSCh. 8.3 - Prob. 49PSCh. 8.3 - Prob. 50PSCh. 8.3 - Prob. 51PSCh. 8.3 - Prob. 52PSCh. 8.3 - Prob. 53PSCh. 8.3 - Prob. 54PSCh. 8.3 - Prob. 55PSCh. 8.3 - Prob. 56PSCh. 8.3 - Prob. 57PSCh. 8.3 - Prob. 58PSCh. 8.3 - Prob. 59PSCh. 8.3 - Prob. 60PSCh. 8.4 - Prob. 1PSCh. 8.4 - Prob. 2PSCh. 8.4 - Prob. 3PSCh. 8.4 - Prob. 4PSCh. 8.4 - Prob. 5PSCh. 8.4 - Prob. 6PSCh. 8.4 - Prob. 7PSCh. 8.4 - Prob. 8PSCh. 8.4 - Prob. 9PSCh. 8.4 - Prob. 10PSCh. 8.4 - Prob. 11PSCh. 8.4 - Prob. 12PSCh. 8.4 - Prob. 13PSCh. 8.4 - Prob. 14PSCh. 8.4 - Prob. 15PSCh. 8.4 - Prob. 16PSCh. 8.4 - Prob. 17PSCh. 8.4 - Prob. 18PSCh. 8.4 - Prob. 19PSCh. 8.4 - Prob. 20PSCh. 8.4 - Prob. 21PSCh. 8.4 - Prob. 22PSCh. 8.4 - Prob. 23PSCh. 8.4 - Prob. 24PSCh. 8.4 - Prob. 25PSCh. 8.4 - Prob. 26PSCh. 8.4 - Prob. 27PSCh. 8.4 - Prob. 28PSCh. 8.4 - Prob. 29PSCh. 8.4 - Prob. 30PSCh. 8.4 - Prob. 31PSCh. 8.4 - Prob. 32PSCh. 8.4 - Prob. 33PSCh. 8.4 - Prob. 34PSCh. 8.4 - Prob. 35PSCh. 8.4 - Prob. 36PSCh. 8.4 - Prob. 37PSCh. 8.4 - Prob. 38PSCh. 8.4 - Prob. 39PSCh. 8.4 - Prob. 40PSCh. 8.4 - Prob. 41PSCh. 8.4 - Prob. 42PSCh. 8.4 - Prob. 43PSCh. 8.4 - Prob. 44PSCh. 8.4 - Prob. 45PSCh. 8.4 - Prob. 46PSCh. 8.4 - Prob. 47PSCh. 8.4 - Prob. 48PSCh. 8.4 - Prob. 49PSCh. 8.4 - Prob. 50PSCh. 8.4 - Prob. 51PSCh. 8.4 - Prob. 52PSCh. 8.4 - Prob. 53PSCh. 8.4 - Prob. 54PSCh. 8.4 - Prob. 55PSCh. 8.4 - Prob. 56PSCh. 8.4 - Prob. 57PSCh. 8.4 - Prob. 58PSCh. 8.4 - Prob. 59PSCh. 8.4 - Prob. 60PSCh. 8.5 - Prob. 1PSCh. 8.5 - Prob. 2PSCh. 8.5 - Prob. 3PSCh. 8.5 - Prob. 4PSCh. 8.5 - Prob. 5PSCh. 8.5 - Prob. 6PSCh. 8.5 - Prob. 7PSCh. 8.5 - Prob. 8PSCh. 8.5 - Prob. 9PSCh. 8.5 - Prob. 10PSCh. 8.5 - Prob. 11PSCh. 8.5 - Prob. 12PSCh. 8.5 - Prob. 13PSCh. 8.5 - Prob. 14PSCh. 8.5 - Prob. 15PSCh. 8.5 - Prob. 16PSCh. 8.5 - Prob. 17PSCh. 8.5 - Prob. 18PSCh. 8.5 - Prob. 19PSCh. 8.5 - Prob. 20PSCh. 8.5 - Prob. 21PSCh. 8.5 - Prob. 22PSCh. 8.5 - Prob. 23PSCh. 8.5 - Prob. 24PSCh. 8.5 - Prob. 25PSCh. 8.5 - Prob. 26PSCh. 8.5 - Prob. 27PSCh. 8.5 - Prob. 28PSCh. 8.5 - Prob. 29PSCh. 8.5 - Prob. 30PSCh. 8.5 - Prob. 31PSCh. 8.5 - Prob. 32PSCh. 8.5 - Prob. 33PSCh. 8.5 - Prob. 34PSCh. 8.5 - Prob. 35PSCh. 8.5 - Prob. 36PSCh. 8.5 - Prob. 37PSCh. 8.5 - Prob. 38PSCh. 8.5 - Prob. 39PSCh. 8.5 - Prob. 40PSCh. 8.5 - Prob. 41PSCh. 8.5 - Prob. 42PSCh. 8.5 - Prob. 43PSCh. 8.5 - Prob. 44PSCh. 8.5 - Prob. 45PSCh. 8.5 - Prob. 46PSCh. 8.5 - Prob. 47PSCh. 8.5 - Prob. 48PSCh. 8.5 - Prob. 49PSCh. 8.5 - Prob. 50PSCh. 8.5 - Prob. 51PSCh. 8.5 - Prob. 52PSCh. 8.5 - Prob. 53PSCh. 8.5 - Prob. 54PSCh. 8.5 - Prob. 55PSCh. 8.5 - Prob. 56PSCh. 8.5 - Prob. 57PSCh. 8.5 - Prob. 58PSCh. 8.5 - Prob. 59PSCh. 8.5 - Prob. 60PSCh. 8.6 - Prob. 1PSCh. 8.6 - Prob. 2PSCh. 8.6 - Prob. 3PSCh. 8.6 - Prob. 4PSCh. 8.6 - Prob. 5PSCh. 8.6 - Prob. 6PSCh. 8.6 - Prob. 7PSCh. 8.6 - Prob. 8PSCh. 8.6 - Prob. 9PSCh. 8.6 - Prob. 10PSCh. 8.6 - Prob. 11PSCh. 8.6 - Prob. 12PSCh. 8.6 - Prob. 13PSCh. 8.6 - Prob. 14PSCh. 8.6 - Prob. 15PSCh. 8.6 - Prob. 16PSCh. 8.6 - Prob. 17PSCh. 8.6 - Prob. 18PSCh. 8.6 - Prob. 19PSCh. 8.6 - Prob. 20PSCh. 8.6 - Prob. 21PSCh. 8.6 - Prob. 22PSCh. 8.6 - Prob. 23PSCh. 8.6 - Prob. 24PSCh. 8.6 - Prob. 25PSCh. 8.6 - Prob. 26PSCh. 8.6 - Prob. 27PSCh. 8.6 - Prob. 28PSCh. 8.6 - Prob. 29PSCh. 8.6 - Prob. 30PSCh. 8.6 - Prob. 31PSCh. 8.6 - Prob. 32PSCh. 8.6 - Prob. 33PSCh. 8.6 - Prob. 34PSCh. 8.6 - Prob. 35PSCh. 8.6 - Prob. 36PSCh. 8.6 - Prob. 37PSCh. 8.6 - Prob. 38PSCh. 8.6 - Prob. 39PSCh. 8.6 - Prob. 40PSCh. 8.6 - Prob. 41PSCh. 8.6 - Prob. 42PSCh. 8.6 - Prob. 43PSCh. 8.6 - Prob. 44PSCh. 8.6 - Prob. 45PSCh. 8.6 - Prob. 46PSCh. 8.6 - Prob. 47PSCh. 8.6 - Prob. 48PSCh. 8.6 - Prob. 49PSCh. 8.6 - Prob. 50PSCh. 8.6 - Prob. 51PSCh. 8.6 - Prob. 52PSCh. 8.6 - Prob. 53PSCh. 8.6 - Prob. 54PSCh. 8.6 - Prob. 55PSCh. 8.6 - Prob. 56PSCh. 8.6 - Prob. 57PSCh. 8.6 - Prob. 58PSCh. 8.6 - Prob. 59PSCh. 8.6 - Prob. 60PSCh. 8.7 - Prob. 1PSCh. 8.7 - Prob. 2PSCh. 8.7 - Prob. 3PSCh. 8.7 - Prob. 4PSCh. 8.7 - Prob. 5PSCh. 8.7 - Prob. 6PSCh. 8.7 - Prob. 7PSCh. 8.7 - Prob. 8PSCh. 8.7 - Prob. 9PSCh. 8.7 - Prob. 10PSCh. 8.7 - Prob. 11PSCh. 8.7 - Prob. 12PSCh. 8.7 - Prob. 13PSCh. 8.7 - Prob. 14PSCh. 8.7 - Prob. 15PSCh. 8.7 - Prob. 16PSCh. 8.7 - Prob. 17PSCh. 8.7 - Prob. 18PSCh. 8.7 - Prob. 19PSCh. 8.7 - Prob. 20PSCh. 8.7 - Prob. 21PSCh. 8.7 - Prob. 22PSCh. 8.7 - Prob. 23PSCh. 8.7 - Prob. 24PSCh. 8.7 - Prob. 25PSCh. 8.7 - Prob. 26PSCh. 8.7 - Prob. 27PSCh. 8.7 - Prob. 28PSCh. 8.7 - Prob. 29PSCh. 8.7 - Prob. 30PSCh. 8.7 - Prob. 31PSCh. 8.7 - Prob. 32PSCh. 8.7 - Prob. 33PSCh. 8.7 - Prob. 34PSCh. 8.7 - Prob. 35PSCh. 8.7 - Prob. 36PSCh. 8.7 - Prob. 37PSCh. 8.7 - Prob. 38PSCh. 8.7 - Prob. 39PSCh. 8.7 - Prob. 40PSCh. 8.7 - Prob. 41PSCh. 8.7 - Prob. 42PSCh. 8.7 - Prob. 43PSCh. 8.7 - Prob. 44PSCh. 8.7 - Prob. 45PSCh. 8.7 - Prob. 46PSCh. 8.7 - Prob. 47PSCh. 8.7 - Prob. 48PSCh. 8.7 - Prob. 49PSCh. 8.7 - Prob. 50PSCh. 8.7 - Prob. 51PSCh. 8.7 - Prob. 52PSCh. 8.7 - Prob. 53PSCh. 8.7 - Prob. 54PSCh. 8.7 - Prob. 55PSCh. 8.7 - Prob. 56PSCh. 8.7 - Prob. 57PSCh. 8.7 - Prob. 58PSCh. 8.7 - Prob. 59PSCh. 8.7 - Prob. 60PSCh. 8.8 - Prob. 1PSCh. 8.8 - Prob. 2PSCh. 8.8 - Prob. 3PSCh. 8.8 - Prob. 4PSCh. 8.8 - Prob. 5PSCh. 8.8 - Prob. 6PSCh. 8.8 - Prob. 7PSCh. 8.8 - Prob. 8PSCh. 8.8 - Prob. 9PSCh. 8.8 - Prob. 10PSCh. 8.8 - Prob. 11PSCh. 8.8 - Prob. 12PSCh. 8.8 - Prob. 13PSCh. 8.8 - Prob. 14PSCh. 8.8 - Prob. 15PSCh. 8.8 - Prob. 16PSCh. 8.8 - Prob. 17PSCh. 8.8 - Prob. 18PSCh. 8.8 - Prob. 19PSCh. 8.8 - Prob. 20PSCh. 8.8 - Prob. 21PSCh. 8.8 - Prob. 22PSCh. 8.8 - Prob. 23PSCh. 8.8 - Prob. 24PSCh. 8.8 - Prob. 25PSCh. 8.8 - Prob. 26PSCh. 8.8 - Prob. 27PSCh. 8.8 - Prob. 28PSCh. 8.8 - Prob. 29PSCh. 8.8 - Prob. 30PSCh. 8.8 - Prob. 31PSCh. 8.8 - Prob. 32PSCh. 8.8 - Prob. 33PSCh. 8.8 - Prob. 34PSCh. 8.8 - Prob. 35PSCh. 8.8 - Prob. 36PSCh. 8.8 - Prob. 37PSCh. 8.8 - Prob. 38PSCh. 8.8 - Prob. 39PSCh. 8.8 - Prob. 40PSCh. 8.8 - Prob. 41PSCh. 8.8 - Prob. 42PSCh. 8.8 - Prob. 43PSCh. 8.8 - Prob. 44PSCh. 8.8 - Prob. 45PSCh. 8.8 - Prob. 46PSCh. 8.8 - Prob. 47PSCh. 8.8 - Prob. 48PSCh. 8.8 - Prob. 49PSCh. 8.8 - Prob. 50PSCh. 8.8 - Prob. 51PSCh. 8.8 - Prob. 52PSCh. 8.8 - Prob. 53PSCh. 8.8 - Prob. 54PSCh. 8.8 - Prob. 55PSCh. 8.8 - Prob. 56PSCh. 8.8 - Prob. 57PSCh. 8.8 - Prob. 58PSCh. 8.8 - Prob. 59PSCh. 8.8 - Prob. 60PSCh. 8 - Prob. 1PECh. 8 - Prob. 2PECh. 8 - Prob. 3PECh. 8 - Prob. 4PECh. 8 - Prob. 5PECh. 8 - Prob. 6PECh. 8 - Prob. 7PECh. 8 - Prob. 8PECh. 8 - Prob. 9PECh. 8 - Prob. 10PECh. 8 - Prob. 11PECh. 8 - Prob. 12PECh. 8 - Prob. 13PECh. 8 - Prob. 14PECh. 8 - Prob. 15PECh. 8 - Prob. 16PECh. 8 - Prob. 17PECh. 8 - Prob. 18PECh. 8 - Prob. 19PECh. 8 - Prob. 20PECh. 8 - Prob. 21PECh. 8 - Prob. 22PECh. 8 - Prob. 23PECh. 8 - Prob. 24PECh. 8 - Prob. 25PECh. 8 - Prob. 26PECh. 8 - Prob. 27PECh. 8 - Prob. 28PECh. 8 - Prob. 29PECh. 8 - Prob. 30PECh. 8 - Prob. 1SPCh. 8 - Prob. 2SPCh. 8 - Prob. 3SPCh. 8 - Prob. 4SPCh. 8 - Prob. 5SPCh. 8 - Prob. 6SPCh. 8 - Prob. 7SPCh. 8 - Prob. 8SPCh. 8 - Prob. 9SPCh. 8 - Prob. 10SPCh. 8 - Prob. 11SPCh. 8 - Prob. 12SPCh. 8 - Prob. 13SPCh. 8 - Prob. 14SPCh. 8 - Prob. 15SPCh. 8 - Prob. 16SPCh. 8 - Prob. 17SPCh. 8 - Prob. 18SPCh. 8 - Prob. 19SPCh. 8 - Prob. 20SPCh. 8 - Prob. 21SPCh. 8 - Prob. 22SPCh. 8 - Prob. 23SPCh. 8 - Prob. 24SPCh. 8 - Prob. 25SPCh. 8 - Prob. 26SPCh. 8 - Prob. 27SPCh. 8 - Prob. 28SPCh. 8 - Prob. 29SPCh. 8 - Prob. 30SPCh. 8 - Prob. 31SPCh. 8 - Prob. 32SPCh. 8 - Prob. 33SPCh. 8 - Prob. 34SPCh. 8 - Prob. 35SPCh. 8 - Prob. 36SPCh. 8 - Prob. 37SPCh. 8 - Prob. 38SPCh. 8 - Prob. 39SPCh. 8 - Prob. 40SPCh. 8 - Prob. 41SPCh. 8 - Prob. 42SPCh. 8 - Prob. 43SPCh. 8 - Prob. 44SPCh. 8 - Prob. 45SPCh. 8 - Prob. 46SPCh. 8 - Prob. 47SPCh. 8 - Prob. 48SPCh. 8 - Prob. 49SPCh. 8 - Prob. 50SPCh. 8 - Prob. 51SPCh. 8 - Prob. 52SPCh. 8 - Prob. 53SPCh. 8 - Prob. 54SPCh. 8 - Prob. 55SPCh. 8 - Prob. 56SPCh. 8 - Prob. 57SPCh. 8 - Prob. 58SPCh. 8 - Prob. 59SPCh. 8 - Prob. 60SPCh. 8 - Prob. 61SPCh. 8 - Prob. 62SPCh. 8 - Prob. 63SPCh. 8 - Prob. 64SPCh. 8 - Prob. 65SPCh. 8 - Prob. 66SPCh. 8 - Prob. 67SPCh. 8 - Prob. 68SPCh. 8 - Prob. 69SPCh. 8 - Prob. 70SPCh. 8 - 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Prob. 27CRPCh. 8 - Prob. 28CRPCh. 8 - Prob. 29CRPCh. 8 - Prob. 30CRPCh. 8 - Prob. 31CRPCh. 8 - Prob. 32CRPCh. 8 - Prob. 33CRPCh. 8 - Prob. 34CRPCh. 8 - Prob. 35CRPCh. 8 - Prob. 36CRPCh. 8 - Prob. 37CRPCh. 8 - Prob. 38CRPCh. 8 - Prob. 39CRPCh. 8 - Prob. 40CRPCh. 8 - Prob. 41CRPCh. 8 - Prob. 42CRPCh. 8 - Prob. 43CRPCh. 8 - Prob. 44CRPCh. 8 - Prob. 45CRPCh. 8 - Prob. 46CRPCh. 8 - Prob. 47CRPCh. 8 - Prob. 48CRPCh. 8 - Prob. 49CRPCh. 8 - Prob. 50CRPCh. 8 - Prob. 51CRPCh. 8 - Prob. 52CRPCh. 8 - Prob. 53CRPCh. 8 - Prob. 54CRPCh. 8 - Prob. 55CRPCh. 8 - Prob. 56CRPCh. 8 - Prob. 57CRPCh. 8 - Prob. 58CRPCh. 8 - Prob. 59CRPCh. 8 - Prob. 60CRP
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- 4. Use the definition to show that the following sequences are Cauchy: (a) {3n²+2}=1 (b) {}=1 2n (c) {n²² +1}n=1arrow_forward10. Determine the sequence generated by each of the following exponential generating func- tions. a) f(x) = 3e3 c) f(x) = ex² e) f(x) = 1 b) f(x)=6e5-3e2x d) f(x) = e2-3x3+5x²+7x f) f(x) = 13³ + ex 1-2xarrow_forward4. Find the limit of the sequence an = 2arctann n³ +4arrow_forward
- 12. Suppose the sequence ao, aj, a2, a3, ... is defined as follows: ao = 0, aj = 1, and for n > 2, a, = 2a,-1 - an-2 + 2. (a) Find a2, a3, a4 and as. (b) Conjecture a formula for a, Vn e NU{0}. (c) Prove your conjecture from (b). %3Darrow_forward4. Write the first 6 terms of the following recursive sequences. (a) an 10an-1 for n ≥ 1 with a₁ = 10. (b) an= 3an-1+2 for n ≥ 2 with a₁ = 1. (c) an = n(an-1 + an-2) for n ≥ 3 with a₁ = 0 and a2 = 1. (d) an = n k=1 ak-1an-k for n ≥ 1 with ao = 1.arrow_forward8. Given the recursive sequence ɑn 3. an-1 - 2· an-2, where ao = 0, a1 = 1, %3D (a) Find a2, a3, a4, a5, a6 using the recurrence relation.arrow_forward
- 14. Consider the sequence convergent, to what? n = 3n+7 Determine whether this sequence is convergent or divergent. Ifarrow_forward13.8. Determine the generating function of the sequence (1,-1, 1,-1, 1,-1,...) in closed form (that is, the generating function should be given as a rational function).arrow_forwardBook Problem 15 Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "INF" (without the quotation marks). If it diverges to negative infinity, state your answer as "MINF". If it diverges without being infinity or negative infinity, state your answer as "DIV". an= b₁ = (-1)"n³ 2n5+8n² + 2 (-1)"n7 2n7+8n²+2arrow_forward
- 8. Suppose that ho, hị, h2, . . is a sequence defined as follows: họ = 1, h = 2, h = 3, hx = hg-1+hx-2+ hỵ-3 for each integer k> 3. a. Prove that h, < 3" for every integer n 2 0.arrow_forwardProblem 2: Consider a sequence defined recursively as To = 1, T₁ = 2, and T₁ = Tn-1 +37-2 for n > 2. Prove that T₁ = O(2.5") and T₁ = 2(2.25"). Hint: First, prove by induction that-2.25"arrow_forwardProblem 3: Define the integer sequences (n)-1 and (yn) by Xn+Yn √2 = (3+2√2)" (So x₁ = 3 and y₁ = 2. And since (3+2√2)² = 17 + 12√2, we get x₂ = 17 and y2 = 12. Etc.) Show that x² - 2y² = 1 for all n € N.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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