- #1

Mr Davis 97

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- 44

## Homework Statement

Let ##x_1=1## and ##\displaystyle x_{n+1} = 3 x_n^2## for ##n \ge 1##.

a) Show if ##a = \lim x_n##, then ##a = 1/3## or ##a = 0##.

b) Does ##\lim x_n## actually exist?

## Homework Equations

## The Attempt at a Solution

I have proven before that, in general, ##\lim s_{n+1} = \lim s_n##. Hence to answer a), we simply take the limit of both sides and solve the quadratic equation. Easy. But clearly, since ##x_n## is not bounded, the limit doesn't actually exist. Why am I getting values ##1/3## or ##0## when the limit doesn't actually exist?