# 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.
• Nirenberg

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

• Timtimtim

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.

• Nirenberg

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

• Timtimtim

Thanks Philip

• Nirenberg

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

Answers can be viewed only if
1. The questioner was satisfied and accepted the answer, or
2. The answer was disputed, but the judge evaluated it as 100% correct.
• Nirenberg