Solve summation problem: $\sum_{k=1}^{n} \tfrac{2k+1}{k^{2}(k+1)^2 } $
$\sum_{k=1}^{n} \tfrac{2k+1}{k^{2}(k+1)^2 } $
This is for a discrete math course. Lots of students were strugglign with this one, so the instructor gave us a couple hints: first, we are supposed to use fractional decomposition before being able to use the telescoping method for actually coming up with the sum. That's all I know.
This is for a discrete math course. Lots of students were strugglign with this one, so the instructor gave us a couple hints: first, we are supposed to use fractional decomposition before being able to use the telescoping method for actually coming up with the sum. That's all I know.

There seems to be a typo in the statement of the problem. Please check the parentheses .

Just fixed it, but I accidentally made the deadline 1 day and 2 hours instead of 2 hours, which I can't adjust. So if anyone could finish this before 2:30 AM EST I would definitely appreciate. I added the relatively large bounty because of the short deadline.

Sure. I will submit a solution before 2:30 AM EST.

Thanks Philip

BE more careful when posting questions, You can not change the deadline to an earlier time after posting.
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