Compute $$\sum_{n=0}^{\infty}\frac{n}{n^4+n^2+1}.$$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Compute $$\sum_{n=0}^{\infty}\frac{n}{n^4+n^2+1}.$$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{2}
Compute $$\sum_{n=0}^{\infty}\frac{n}{n^4+n^2+1}.$$
train