Question

(1-1/2²)×(1-1/3²)×···×(1-1/9²)×(1-1/10²)

Answer 1

1-1/n^2=(n^2-1)/n^2=(n-1)(n+1)/n^2=(n-1)/n * (n+1)/n

如：(1-1/2²)=1/2 * 3/2

(1-1/3²)=2/3 * 4/3

(1-1/9²)=8/9 *10/9

(1-1/10²)=9/10 * 11/10

可知中间项都消去了,只剩了1/2 与 11/10

所以结果为11/20