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# HELP :( Watch

1. I'm having some issues with a numbers and sets example sheet..
Firstly, is there a method to test whether a series converges? For example n!/n^n.

Also if sum(x_n) is a divergent series, how would i show that there exists a divergent series sum(y_n) with y_n > 0 for all n such that y_n/x_n tends to 0.

Lastly, is there an enumeration of Q (rationals) as q_1, q_2, q_3,... such that sum(q_n - q_n+1)^2 converges?

This is for an example sheet so hints would be appreciated. Thanks
2. (Original post by cmhcgs815)
I'm having some issues with a numbers and sets example sheet..
Firstly, is there a method to test whether a series converges? For example n!/n^n.

This is for an example sheet so hints would be appreciated. Thanks
There are many tests to help verify the convergence of a series: Null sequence test, comparison test, ratio test and integral test are what come to mind. For your example, if (a_n) does not tend to zero, then diverges. From having seen n!/n^n previously, you should be able to tell whether the sequence converges or diverges.

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Updated: December 26, 2010
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