User:Saiyr

From Wikipedia, the free encyclopedia

\Pi_{i=2}^{n}(1-\frac{1}{n^{2}})=\frac{n+1}{2n}

\frac{n+1}{2n}(1-\frac{1}{(n+1)^{2}})

\frac{n+1}{2n}-\frac{n+1}{2n(n+1)^{2}}=\frac{(n+1)^{3}-(n+1)}{2n(n+1)^{2}}=\frac{(n+1)^{2}-1)}{2n(n+1)}=\frac{n^{2}+2n}{2n(n+1)}=\frac{(n+1)+1}{2(n+1}