Question about $a_n=\sum_{k=1}^n \frac{n}{n^2+k}\ $for $ n \in\mathbb{N}$
Hint
Prove these inequalities $$b_n=n\times \frac{n}{n^2+n}\le a_n\le n\times \frac{n}{n^2+1}=c_n$$ What's the limit of $(b_n)$ and $(c_n)$ and conclude.
Question about $a_n=\sum_{k=1}^n \frac{n}{n^2+k}\ $for $ n \in\mathbb{N}$
Hint
Prove these inequalities $$b_n=n\times \frac{n}{n^2+n}\le a_n\le n\times \frac{n}{n^2+1}=c_n$$ What's the limit of $(b_n)$ and $(c_n)$ and conclude.