Word Count : 238

---

We are asked to evaluate $$ \lim_{n\to\infty} \left[ \frac{n+1}{n^2+1^2} + \frac{n+2}{n^2+2^2} + \frac{n+3}{n^2+3^2} + \cdots + \frac{n+n}{n^2+n^2} \right] $$ using Cauchy’s integral test (which essentially compares a sum with an integral in the limit). Let’s solve step by step. --- Step 1: Rewrite the sum in a _______ _____ ___ _____ ____ _____ ____.
____ _______ _______ _________ ______ ______ _____ _________ __________ ____.
____ ________ __________ ___ ________ ________ ______ ______.
_____ ____ ______ ______ _____ _____ _______ _______ _____.
____ ________ __________ ___ ______ _______ __________ ___ _________ ________.
__________ _____ ____ _____ ____ _________ ______ ___ ________ _________ ________.
_________ _________ ________ ______ _________ ____ ________ _____ ________ ________ _____ _________.
________ ____ _________ _____ ______ _____.
___ ___ __________ _____ ___ _______ ________ ______ ________ ______ ____ _______.
__________ _____ _______ _______ ________ ______.
___ __________ __________ ____ __________ ___ ____ _______ ____ __________ ______.
____ __________ ___ _____ __________ _____ ________ _______ ______.
_____ ____ ___ _____ ____ _______ ___ _____ ______ ________ _______.
_________ _________ _______ _____ _____ ___ ___ ________ ______.
______ _________ _________ ________ _______ ______ ______ __________ ________.
__________ _________ ___ _____ __________ __________ _______ _______ ________ _____ ____.
__________ ___ _________ ______ ________ ___.
______ _________ _______ ___ ________ _____ ________ ____ _____ _________ _____.
_____ ___ _____ _________ ____ ___.
__________ ________ _________ _______ ___ ______.
_____ ___ __________ ______ _________ ________ _____ _________ ___ _________ _______.
Get Full Answer on WhatsApp