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Solved: Sequences vs. seriesa. Find the limit of .b.

Chapter 1, Problem 44RE

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QUESTION:

Sequences vs. series

a. Find the limit of \(\left\{\frac{1}{k}-\frac{1}{k+1}\right\}\).

b. Evaluate \(\sum_{k=1}^{\infty}\left(\frac{1}{k}-\frac{1}{k+1}\right)\).

Questions & Answers

QUESTION:

Sequences vs. series

a. Find the limit of \(\left\{\frac{1}{k}-\frac{1}{k+1}\right\}\).

b. Evaluate \(\sum_{k=1}^{\infty}\left(\frac{1}{k}-\frac{1}{k+1}\right)\).

ANSWER:

Step 1 of 3

a)

 

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