Suppose \(\displaystyle G_{1} , G_{2} ,...\) are any numbers that satisfy the inequalities
\(\displaystyle 0 < G_{n} < 1\) and \(\displaystyle (1-G_{n})\cdot G_{n+1} > \frac{1}{4}, \;\ \forall n\)
Prove that \(\displaystyle \lim_{n\to \infty}G_{n}\) exists, and ?nd it.
\(\displaystyle 0 < G_{n} < 1\) and \(\displaystyle (1-G_{n})\cdot G_{n+1} > \frac{1}{4}, \;\ \forall n\)
Prove that \(\displaystyle \lim_{n\to \infty}G_{n}\) exists, and ?nd it.