5

Part of 2005 Brazil Undergrad MO

Problems(1)

A nice identity concerning an integral and a serie

Source: Brazilian Math Olympiad 2005, Problem 5

\sum_{n=1}^\infty {1\over n^n} = \int_0^1 x^{-x}\,dx.

calculusintegrationlogarithmsfunctioninductionreal analysisreal analysis solved