Find $ \lim_{n\to\infty}a_n$ where $ (a_n)_{n\ge1}$ is defined by $ a_n=\frac1{\sqrt{n^2+8n-1}}+\frac1{\sqrt{n^2+16n-1}}+\frac1{\sqrt{n^2+24n-1}}+\ldots+\frac1{\sqrt{9n^2-1}}$.
Problem
Source: Moldova National MO 2008, 12 Grade, Problem 6 (Day 2)
Tags: calculus, integration, limit, real analysis, real analysis unsolved