Partial sums Let S, be the nth partial sum of a= 8. Findk=1lim a, and lim S,.

Given Data The sigma notation is ∑k=1∞ak=8. Let Sn and ak be the nth partial sum of ∑k=1∞ak=8. The…

Answered: Partial sums Let S, be the nth partial…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Partial sums Let S, be the nth partial sum of a
= 8. Find
k=1
lim a, and lim S,.

Expert Solution

Step 1

Given Data

The sigma notation is $\sum_{k = 1}^{\infty} a_{k} = 8$ .

Let $S_{n}$ and $a_{k}$ be the nth partial sum of $\sum_{k = 1}^{\infty} a_{k} = 8$ .

The sigma notation is $\sum_{k = 1}^{\infty} a_{k} = 8$ . So it means that the limit of the given series is converges.

As a result $\lim_{n \to \infty} a_{k} = 0$ .

Hence the value of limit $\lim_{n \to \infty} a_{k} = 0$ .

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Partial sums Let S, be the nth partial sum of a = 8. Find k=1 lim a, and lim S,.