- #1

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- Homework Statement:
- calculate the limit of a phrase

- Relevant Equations:
- limit

Hi

I was working on a physics problem and it was almost solved.

Only the part that is mostly mathematical remains, and no matter how hard I tried, I could not solve it.

I hope you can help me.

This is the equation I came up with and I wanted to prove it: $$\lim_{n \rightarrow+ \infty} { \sum_{i=1}^n \frac 1 {\sqrt{i(2n-i-1)} +\sqrt{i(2n-i)}}}=\frac \pi 4$$

I was working on a physics problem and it was almost solved.

Only the part that is mostly mathematical remains, and no matter how hard I tried, I could not solve it.

I hope you can help me.

This is the equation I came up with and I wanted to prove it: $$\lim_{n \rightarrow+ \infty} { \sum_{i=1}^n \frac 1 {\sqrt{i(2n-i-1)} +\sqrt{i(2n-i)}}}=\frac \pi 4$$