_ n (1- 1 2^2 ) (1- 1 3^2 ) (1- 1 4^2 ) (1- 1 n^2 )

MATHEMATICS · Subjective · AoPS · Mathematics · Sequences & Series · Sequences & Series

Problem

\lim_{n\to\infty}\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right)\cdots\left(1-\frac{1}{n^2}\right)