Consider $f(N)=1-\frac1N \sum_{k=1}^N (\frac{k-1}{N})^n\quad,n,N\in \mathbb N $. Why does $\lim_{N\to\infty}f(N)=1-\int_0^1 x^ndx$
In the text I was reading this is just stated without any explanation. Why is this true?
2026-04-29 19:06:28.1777489588
integral as limit of a sum
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