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.

A telescoping series:
$\sum_{n=1}^{k} f(n) - f(n+1) = f(1) - f(k+1)$
How do we get our series into that form?
$(n^4 + n^2 + 1) = (n^2+n +1)(n^2-n+1)\\
\frac {n}{(n^4 + n^2 + 1)} = \frac {1}{2(n^2 - n + 1)} - \frac {1}{2(n^2 + n + 1)}$
Here is the really tricky bit:
$\frac {1}{(n^2 + n + 1)} = \frac {1}{(n+1)^2 - (n+1) + 1}$
$\sum_{n=1}^{k}\frac {n}{n^4 + n^2 + 1} = \frac 12 - \frac {1}{2(k^2+k+1)}$
