u-u-u-1-3-u-1-4-u-1-5-

Question Number 144877 by imjagoll last updated on 30/Jun/21

u + \sqrt{u} + \sqrt[3]{u} + \sqrt[4]{u} + \sqrt[5]{u} + \dots + \infty = ?

Answered by MJS_new last updated on 30/Jun/21

\forall u > 0 : \underset{n = 1}{\sum^{\infty}} u^{1 / n} = + \infty

easy to see because \lim_{n \to + \infty} u^{1 / n} = 1

Commented by imjagoll last updated on 30/Jun/21

thank you sir