   Chapter 11.2, Problem 5E

Chapter
Section
Textbook Problem

Calculate the first eight terms of the sequence of partial sums correct to four decimal places. Does it appear that the series is convergent or divergent? ∑ n = 1 ∞ 1 n 4 + n 2

To determine

To calculate:

The first eight terms of the sequence of the partial sums correct to four decimal places and then conclude if the series is convergent or divergent.

Explanation

1) Concept:

Use the definition of the convergent series

2) Definition:

A series n=1an is convergent if the sequence {sn} is convergent and limnsn=s exists as a real number.

3) Given:

n=11n4+n2

4) Calculation:

Consider

an=1n4+n2

s1=a1=11+1=12=0.5

s2=s1+a2=12+120=0.5+0.05=0.55

s3=s2+a3=0.55+134+320.5611

s4=s3+a4=0.5611+144+420.5648

s5=s4+a5=0.5648+154+520

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