Found this question...by a dude named Vikram Singh (Yeah give you some recognition).

Question

anonymous · Answer

its a dot

anonymous · Answer

m is a positive integer such that

$$f(x) = \sum_{k=1}^{\infty} \frac{ x^m }{ (1+x^4)^{k-1} }$$

Given that f(x) is continuous at x = 0, find the smallest possible value of m.

kainui · Answer

Well I'd probably change it to just start out at k=0 and change that exponent to k instead of k-1 just because that's annoying... Uhhh... Since x^m is independent of the sum, just pull it outside and take the derivative with respect to m I guess and set it equal to zero? I don't know I gotta go sorry good luck!

kainui · Answer

Well once you pull the x^m out it becomes a geometric series. Plug it in, x^m*1/(1-(1/(1-x^4))) you end up with x^m(1-x^-4) so now solve for nonnegative exponent, m-4=0.

anonymous · Answer

Thank you Gauss!