$\displaystyle \sum _{k=1}^{\infty }{\frac {{5}^{k}}{{3}^{k}+{4}^{k}}}$

I'm thinking this is a geometric, but I can't seem to reorder it. Any tips on what I should do?

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- Apr 27th 2010, 08:51 PMCalculusCrazedDivergence/convergence
$\displaystyle \sum _{k=1}^{\infty }{\frac {{5}^{k}}{{3}^{k}+{4}^{k}}}$

I'm thinking this is a geometric, but I can't seem to reorder it. Any tips on what I should do? - Apr 27th 2010, 09:11 PMmaddas
$\displaystyle {5^k\over 3^k + 4^k} \ge {5^k\over 4^k+4^k}$

- Apr 27th 2010, 09:21 PMCalculusCrazed
Ahh, thank you! That worked out very nicely. (Happy)