I have 2 questions I am having problems with.(adsbygoogle = window.adsbygoogle || []).push({});

The goal is to determine if the series converges or not.

Q1: Sum from(1 to inf) of (exp^i)/( (exp^2i) + 9)

I tried to do the integral test but I cannot seem to integrate. Any guides would be appreciated.

Also if I wanted to compare it what would I compare it to.

Q2: Sum from (2 to inf) of 1/( (i^2) - 1)

I did the integral test and came out to the following

integral of 1/i^2 -1 = 1/2 (ln(i-1) - ln(i+1))

So in looking at this as i approaches infinity, can I say that integral approaches 0 and therefore this series converges.

All help is appreciated.

Thanks

Asif

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# Infinite series- converges or not

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