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

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Calculus

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

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter8: Sequences And Series

Section8.1: Sequences And Summation Notation

Problem 44E

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Question

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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