1. Convergence test..

I'm looking for a nice (full) proof of some convergence test,
Including...
$\Sigma a_k$ and $\Sigma 2^ka_{2^k}$

2. Originally Posted by Also sprach Zarathustra
I'm looking for a nice (full) proof of some convergence test,
Including...
$\Sigma a_k$ and $\Sigma 2^ka_{2^k}$

Cauchy Condensation Test

Tonio

3. I'd also like to point out that Cauchy Condensation Test is a generalization of Oresme's proof of the divergence of the harmonic series. It might be useful to have a look.

Harmonic series (mathematics) - Wikipedia, the free encyclopedia