Word Count : 191

---

We are given the limit: \[ \lim_{n\to\infty} \left[\frac{n+1}{n^2+1^2}+\frac{n+2}{n^2+2^2}+\frac{n+3}{n^2+3^2}+\cdots+\frac{n+n}{n^2+n^2}\right] \] ### Step 1: Convert to a General Form The given sum can be written as: \[ S_n = \sum_{k=1}^{n} \frac{n+k}{n^2+k^2} \] Rewriting the fraction: \[ \frac{n+k}{n^2+k^2} = \frac{n+k}{n^2(1 + __________ ___ ______ __________ __________ _________.
________ _____ ________ __________ ___ ____ __________ _____.
________ __________ _____ ______ ____ _______ ______ ________ _________ _________ _______.
________ ___ ___ __________ ______ ________ ____ ________ ___ _______ _________.
______ __________ _______ __________ ___ _________ ________ _________ __________ ____.
___ ___ ________ ______ _____ _____ _______ ________ ______.
___ ___ ___ _______ ___ __________ ________ ________ ________ _____.
_____ _____ _____ _______ ____ _______ ____.
_______ ___ ___ __________ __________ ____ ____ ____ __________ __________.
_____ __________ ___ _______ __________.
_______ __________ _________ ____ _______ _________.
___ ______ ______ ___ _____ _____ ___ ___ ______.
_____ _______ ________ _______ __________ _______ __________ ____ ________.
_____ ____ ___ _____ ____ __________ ___ _________ ______ ______.
_________ ______ ________ __________ ____ ____ _____ ______.
_____ _______ ________ ___ _______ _______ ________ __________ ________ _____.
___ _______ ___ ________ __________ _______ ________ _____ _____ __________.
___ ____ _____ __________.
Get Full Answer on WhatsApp