<s>[INST] How to find the sum $\frac{1}{1^4+1^2+1}+\frac{2}{2^4+2^2+1}+..+\frac{2015}{2015^4+2015^2+1}$? How to find the sum $\frac{1}{1^4+1^2+1}+\frac{2}{2^4+2^2+1}+..+\frac{2015}{2015^4+2015^2+1}$ ?
I'm not being able to approach the problem.Hints please!
 [/INST] You might want to prove by induction that the sum 
$$\sum_{i=1}^n \frac{i}{i^4+i^2+1} = \frac{\frac{1}{2} n(n+1)}{n^2+n+1}$$
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