Bonjour
1+1/n-1/(n+1)=1+(n+1-n)/[n(n+1)]=1+1/[n(n+1)]
Donc
(1+1/n-1/(n+1))²=(1+1/[n(n+1)])²
(1+1/n-1/(n+1))²=1+2/[n(n+1)]+1/[n²(n+1)²]
(1+1/n-1/(n+1))²=1+2n(n+1)/[n²(n+1)²]+1/[n²(n+1)²]
(1+1/n-1/(n+1))²=1+(2n²+2n+1)/[n²(n+1)²]
(1+1/n-1/(n+1))²=1+(n²+n²+2n+1)/[n²(n+1)²]
(1+1/n-1/(n+1))²=1+(n²+(n+1)²)/[n²(n+1)²]
(1+1/n-1/(n+1))²=1+n²/[n²(n+1)²]+(n+1)²/[n²(n+1)²]
(1+1/n-1/(n+1))²=1+1/(n+1)²+1/n²
(1+1/n-1/(n+1))²=1+1/n²+1/(n+1)²