MathDB

Sequence

Source: St Petersburg 2008 10th grade #7

July 29, 2011

inequalitiesinequalities proposed

Problem Statement

In a sequence,

x_1=\frac{1}{2}

and

x_{n+1}=1-x_1x_2x_3...x_n

for

n\ge 1

. Prove that

0.99<x_{100}<0.991

.
Fresh translation. This problem may be similar to one of the 9th grade problems.