Evaluate sum of n terms of the series:
$\displaystyle \frac{8}{5} + \frac{16}{65} + \frac{24}{325} + \mbox{... till n terms}$
Vocabulary problem I meant separate.
The even terms in the form 2k will be $\displaystyle 5^k13^k$
The odd terms in the form 2k+1 will be $\displaystyle 5^{k+1}13^k$
Then, I guess you'll have a different result, depending on whether n is odd or even.
I don't see a shortcut for the moment. And it doesn't look nice