Prove that lim gn for n→∞ exists, and ﬁnd it.

1. Sep 9, 2009

dannysaf

Suppose g1 , g2 ,... are any numbers that satisfy the inequalities
0 < gn < 1 and (1 − gn )gn+1 > 1/4 for all n.

Prove that lim gn for n→∞ exists, and ﬁnd it.

I need well substantiated answer! Thanks.

2. Sep 9, 2009

LCKurtz

Is this a homework problem? I'll give you a hint. Show:

$$\frac 1 {4(1-x)} \ge x$$

on the interval, consequently showing your sequence gn is increasing. Then...