Basic Analysis I — Real Analysis · Problem 2.2.4

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · recursively-defined-sequences

Problem

Suppose

x_1 := \frac{1}{2}

and

x_{n+1} := x_n^2

. Show that

\{x_n\}_{n=1}^\infty

converges and find

\lim_{n\to\infty} x_n

. Hint: You cannot divide by zero!