sum e^n/(1+e^2n) n = 1 to infinity By using the integral test I need to integrate this to determine whether it will converge or diverge. Can someone please help with the integration. I cannot figure out how to integrate it.
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Originally Posted by ur5pointos2slo sum e^n/(1+e^2n) n = 1 to infinity By using the integral test I need to integrate this to determine whether it will converge or diverge. Can someone please help with the integration. I cannot figure out how to integrate it. use substution, let , then Do the rest! show where you are getting stuck
Originally Posted by harish21 use substution, let , then Do the rest! show where you are getting stuck My problem is just that. The derivative of e^n is just e^n dn. What kind of technique would I need to use on this?
Originally Posted by ur5pointos2slo My problem is just that. The derivative of e^n is just e^n dn. What kind of technique would I need to use on this? scratch that stupid me. Ok we are using a u-substitution. I am confused on where to go next. There must be a trick using exponential rules?
Originally Posted by ur5pointos2slo My problem is just that. The derivative of e^n is just e^n dn. What kind of technique would I need to use on this? plug back , you have: now find out if the series converges or not!
Originally Posted by harish21 plug back , you have: now find out if the series converges or not! That seemed too easy. I couldn't see it until you pointed it out. So it equals Pi/4 and it converges.
Originally Posted by ur5pointos2slo That seemed too easy. I couldn't see it until you pointed it out. So it equals Pi/4 and it converges. ?? , This is not equal to
Originally Posted by harish21 ?? oops forgot the exponential...so Pi/2 - tan^-1(e) converges.
Originally Posted by ur5pointos2slo oops forgot the exponential...so Pi/2 - tan^-1(e) converges. Yes!
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