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x_n=\sqrt{x_{n-1}^2+x_{n-1}}+x_{n-1}} ,x_1=1

Source: China Northern MO 2009 p1 CNMO

December 12, 2020
Sequencealgebrarecurrence relation

Problem Statement

Sequence {xnx_n} satisfies: x1=1x_1=1 , xn=xn−12+xn−1+xn−1{x_n=\sqrt{x_{n-1}^2+x_{n-1}}+x_{n-1}} ( n>=2{n>=2} ) Find the general term of {xnx_n}
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