Finding $\frac1{1+1^2+1^4}+\frac2{1+2^2+2^4}+\cdots+\frac n{1+n^2+n^4}$. 
Find an expression for
$$\frac1{1+1^2+1^4}+\frac2{1+2^2+2^4}+\cdots+\frac n{1+n^2+n^4}.$$

This was given in the chapter for APs. However, I do not see how this relates to them. I tried using telescopic sums, but I am not proficient in them and was thererfore unable to solve this question.
I tried calculating the sum for a few consecutive values, and tried constructing a polynomial that covered them all, but it proved to be difficult.
Any hints on how to solve this question?
Please help.

Let $a_k = k/(1+k^2+k^4)$.
Then:
$$a_k =
\underbrace{\frac{k(1-k)}{2(1-k+k^2)}}_{b_k}
+
\underbrace{\frac{k(1+k)}{2(1+k+k^2)}}_{c_k}.$$
Now observe that
$$b_{k+1} = \frac{(k+1)(-k)}{2(-k+(k+1)^2)}
=
\frac{-k(1+k)}{2(1+k+k^2)} = -c_k.$$
Can you conclude?
