(1-1/2²)(-1/3²)(1-1/4²)(1-1/5²)…(1-1/10²)

问题描述:

(1-1/2²)(-1/3²)(1-1/4²)(1-1/5²)…(1-1/10²)

原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/10)(1+1/10)
=1/2 * 2/3 *...*9/10 * 3/2 * 4/3 ...*11/10
=1/2 * 11/10
=11/20