To find Convergence/Divergence of

and of this one

Thank you. :)

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- Jul 19th 2012, 01:47 AMpratique21Convergence Divergence ?
To find Convergence/Divergence of

and of this one

Thank you. :) - Jul 19th 2012, 02:04 AMgirdavRe: Convergence Divergence ?
You should write for the first, not for the whole sum since it won't depend on . Use the fact that . For the second, could you write the terms with a formula on which appears?

- Jul 19th 2012, 02:15 AMpratique21Re: Convergence Divergence ?
I do not understand how the fact that n! >= n(n-1) can be used for to solve this .

The second one can be simplified to get :-

Enlighten me.

:) - Jul 19th 2012, 02:39 AMpratique21Re: Convergence Divergence ?
It is e itself actually, so it converges !

e=

But how do you prove it ? - Jul 19th 2012, 02:41 AMgirdavRe: Convergence Divergence ?
We have and the sum of the terms of the RHS is telescopic.

For the second series, first try ratio test. If you can't conclude, try Raabe-Duhamel test. - Jul 19th 2012, 03:02 AMpratique21Re: Convergence Divergence ?
thanks girdav. I shall try it using the tests you mentioned. However this problem was presented before discussion on ratio test or raabe-duhamel test. So i guess we are expected to solve it using comparison test.