Six Hundred Followers Problem

Calculus Level 2

limn(312+512+22+712+22+32++2n+112+22++n2)= ? \lim_{n \to \infty} \left ( \frac {3}{1^2} + \frac {5}{1^2+2^2} + \frac {7}{1^2+2^2+3^2} + \ldots + \frac {2n+1}{1^2+ 2^2 + \ldots + n^2} \right ) = \ ?

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