JEE Limits 2

Calculus Level 4

\[\displaystyle \lim_{ m \rightarrow \infty } \displaystyle \lim_{n \rightarrow \infty } \left (\dfrac{1+\sqrt[n]{1^n+2^n}+\sqrt[n]{2^n+3^n}+\sqrt[n]{3^n+4^n}+\cdot+\sqrt[n]{(m-1)^n+m^n}}{m^2}\right )\]

This problem is a part of My picks for JEE 1
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