   Chapter 11.2, Problem 4E

Chapter
Section
Textbook Problem

# Calculate the sum of the series ∑ n = 1 ∞ a n whose partial sums are given.4. s n = n 2 − 1 4 n 2 + 1

To determine

To calculate: The sum of the series for the given partial sum.

Explanation

Given:

The partial sum is sn=n214n2+1 .

Result used:

If limnsn=L , then n=1an=L .

Calculation:

Obtain the limit of the partial sum. (The value of the term sn as n tends to infinity).

limnsn=limn(n214n2+1)

Divide the numerator and denominator by n.

limn(n214n2+1)=limn(n21n24n2+1n2)=limn(11n24+1n2)=limn(1)

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