?Determine whether the series is convergent or divergent. \(\sum_{n=1}^{\infty}

Chapter 9, Problem 20

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QUESTION:

Determine whether the series is convergent or divergent.

                     \(\sum_{n=1}^{\infty} \frac{1}{n^{2}+2 n+2}\)

Equation Transcription:

Text Transcription:

sum _n=1^infinity 1/n^2 + 2n + 2

Questions & Answers

QUESTION:

Determine whether the series is convergent or divergent.

                     \(\sum_{n=1}^{\infty} \frac{1}{n^{2}+2 n+2}\)

Equation Transcription:

Text Transcription:

sum _n=1^infinity 1/n^2 + 2n + 2

ANSWER:

Step 1 of 4

The analogous function  is continuous,

positive and decreasing for  so we can use the integral test.

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