Hello, I'm working on this problem:(adsbygoogle = window.adsbygoogle || []).push({});

Prove that for any real x, the series SUM n=2 to infinity of 1/(log n)^x diverges.

So far, I have applied the test that says that if SUM 2^n*a_2n converges then the series converges. I got:

1/log2*SUM 2^n/n^x I know that 1/n^x converges if x>1, but 2^n will explode, so I'd have convergent (sometimes) times divergent = divergent. Can I do that?

Thanks,

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# Divergent series

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