Basic Analysis I — Real Analysis · Problem 2.2.14

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · recursively-defined-sequences

Problem

Suppose x1:=cx_1 := c and xn+1:=xn2+xnx_{n+1} := x_n^2 + x_n. Show that {xn}n=1∞\{x_n\}_{n=1}^\infty converges if and only if −1≤c≤0-1 \leq c \leq 0, in which case it converges to 00.

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