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 8.4, Problem 35PS
To determine
To find: whether the given series converges or not.
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4. The goal of this problem is to justify the following statement by using the Comparison Test
for series.
Suppose that a, and
bm are convergent series with an, b, 20 for all natural numbers
n. Then, a,b, is also a convergent series.
(a)
By only using the Comparison Test and the following fact (FACT 1), justify
2 0 for all a and , is convergent, then is also convergent.
that if
n=1
FACT 1: if a, 2 0 for all na and a, is convergent, then a anb, is alsO convergent.
n=1
3. Show divergence or find the sum of the series
8.
-5h + 32n
11"
n32
8. Find the value (or limit) of the infinite series
1+ 2k
if it exists.
3k-1
k=1
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
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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 - 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- Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+arrow_forward4. The goal of this problem is to justify the following statement by using the Comparison Test for series. Suppose that an and b, are convergent series with an, bn 20 for all natural numbers n=1 n=1 n. Then, anbn is also a convergent series. n=1 (a) By only using the Comparison Test and the following fact (FACT 1), justify that if a, 20 for all n and a, is convergent, then a is also convergent. n=1 n=1 2 FACT 1: if a, > 0 for all n and > an is convergent, then a M for some n=1 natural number M.arrow_forward9. Determine if the series is absolutely convergent, conditionally convergent, or divergent using one of the following (divergence test, integral test, comparison test, limit comparison test, alternating series test, ratio test, root test).arrow_forward
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