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for the sequence an = n / n+1 it is know that it is strictly increasing as n increases. show that this is true by 1) look at the behaviour of the difference of successive terms, an+1 - an and 2) the  same for the ratio of successive terms, an+1 / an

for the sequence an = n / n+1 it is know that it is strictly increasing as n increases. show that this is true by 1) look at the behaviour of the difference of successive terms, an+1 - an and 2) the  same for the ratio of successive terms, an+1 / an

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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for the sequence an = n / n+1 it is know that it is strictly increasing as n increases. show that this is true by
1) look at the behaviour of the difference of successive terms, an+1 - an and 2) the  same for the ratio of successive terms, an+1 / an

Expert Solution
Step 1: Introduction of the given problem

Given sequence a subscript n equals fraction numerator n over denominator n plus 1 end fraction.

We have to show the given sequence is increasing by analyse the behaviour of a subscript n plus 1 end subscript minus a subscript n and a subscript n plus 1 end subscript over a subscript n

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