Let $\displaystyle x_{1} =1 $, and let $\displaystyle x_{n+1} =\frac {(x_1 +x_2 + . . . + x_{n} ) }{2} $. Prove that $\displaystyle x_n \rightarrow \infty $

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I have proved that $\displaystyle x_n $ is a strictly decreasing sequence by induction. Will this help a bit?