Question

Use an appropriate Riemann sum to evaluate the limit
lim((1^5 + 2^5 + 3^5 + ... + n^5)/ (n^6)) as n -> infinity

Answer 1

WILL FAN AND MEDAL

Answer 2

\[\int\limits_{0}^{1}x^5dx=\lim_{n\to\infty}\sum_{i=1}^{n}\left(i\frac{1}{n}\right)^5\frac{1}{n}=\lim_{n\to\infty}\sum_{i=1}^{n}i^5\frac{1}{n^6}\]