Infinite series converges or not
I have 2 questions I am having problems with.
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(i1)  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 
There's an easy comparison for both of them. Q1) compare to exp(i)/exp(2i), Q2) compare to 2/(i^2).

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Dick: thanks for response. I will look at your way. Always good to learn new ways
Tom: This is how I did the integral test Let u = exp^(2x) + 9 du/dx = 2exp^(2x) This is where I got stuck. I thought once I do du/dx, I should get e^x in this equation but since I didn't I couldn't get anywhere. So I tried by integration by parts and went into an infinite loop a let u = 1/( exp(2x) + 9) b du/dx = 2/(exp(2x +9) c let dv = exp^x dx d v = e^x To integrate uv  integral (v wrt dx) integral (e^x/e^2x +9) = e^x/(e^2x + 9) +2 integral (e^x/e^2x +9) This is where I got stuck. Thanks Asif 
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