MathDB

7

Part of 1990 Romania Team Selection Test

Problems(1)

Sequence and floor function

Source: Romania TST 1990

8/6/2009
The sequence (xn)n≥1 (x_n)_{n \geq 1} is defined by: x_1\equal{}1 x_{n\plus{}1}\equal{}\frac{x_n}{n}\plus{}\frac{n}{x_n} Prove that (xn) (x_n) increases and [x_n^2]\equal{}n.
functioninductionalgebra unsolvedalgebra