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$\underset{n \to \infty}{L t} [\frac{1^{m} + 2^{m} + 3^{m} + ..... + n^{m}}{n^{m + 1}}]$

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Correct option is A

limn→∞⁡1n1mnm+2mnm+3mnm+….+nmnm =limn→∞1n∑r=1n rnm=∫01 xmdx=xm+1m+101=1m+1

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Ltn→∞1m+2m+3m+.....+nmnm+1

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$\underset{n \to \infty}{L t} [\frac{1^{m} + 2^{m} + 3^{m} + ..... + n^{m}}{n^{m + 1}}]$