A calculus problem by Jose Sacramento

Calculus Level 4

\[ \lim_{n\to\infty} \left( \dfrac n{n^2 + 1} + \dfrac n{n^2+ 4} + \dfrac n{n^2 + 9} + \cdots + \dfrac n{n^2 + n^2} \right) \]

Find the value of the closed form of the above limit.

Give your answer to 3 decimal places.

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