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.
  • Erdos Erdos
    0

    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.

  • Erdos Erdos
    0

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

  • Thanks Philip

  • Erdos Erdos
    0

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

Answer

Answers can only be viewed under the following conditions:
  1. The questioner was satisfied with and accepted the answer, or
  2. The answer was evaluated as being 100% correct by the judge.
View the answer
Erdos Erdos
4.7K
  • Erdos Erdos
    0

    Leave a comment if you need any clarifications.

The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to a 50% commission on every question that your affiliated users ask or answer.