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HELP :(

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 :smile:

Reply 1

Clarity Incognito

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 :smile:

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