Will You Find the 100th Power Sum Formula?

Calculus Level 3

limn1100+2100+3100+4100++n100n101=AB\large \lim_{n \to \infty} \frac{1^{100} + 2^{100} + 3^{100} + 4^{100} +\cdots +n^{100}}{n^{101}} = \frac{A}{B} .

If AA and BB are coprime positive integers, find A+BA+B.

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