Bourbaki

Exercise 10, § 4

Functions of a Real Variable, V, p. 51

For every number α>0\alpha > 0, prove the formula

1αn+2αn+⋯+nαn∼nαn1−e−α 1^{\alpha n} + 2^{\alpha n} + \cdots + n^{\alpha n} \sim \frac{n^{\alpha n}}{1 - e^{-\alpha}}
when nn tends to +∞+\infty.

Solution

No solution has been written yet.

Machine translation of the English, by gpt-5-mini. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.