   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?5. ∑ n = 1 ∞ 1 n 4 + n 2

To determine

To calculate: The first eight terms of the sequence of the partial sums and use them to check whether the series is convergent or divergent.

Explanation

Given:

The series is n=11n4+n2 .

Here, an=1n4+n2 .

Calculation:

The nth term of the partial sum is sn=i=1nai .

Obtain the first eight terms of the sequence of the partial sums.

 N n4+n2 an=1n4+n2 sn=∑i=1nai 1 14+12=2 a1=0.5 s1=0.5 2 24+22=20 a2=0.05 s2=0.55 3 34+32=30 a3=0

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