6

Part of 1985 IMO Shortlist

Problems(1)

IMO Long List 1986 inequality for x_i

Source:

x_n = \sqrt[2]{2+\sqrt[3]{3+\cdots+\sqrt[n]{n}}}.

Prove that x_{n+1}-x_n <\frac{1}{n!} n=2,3,\cdots

algebraSequenceInequalitycalculusrecurrence relationIMO Shortlistinequalities