(1-½²)(1-⅓²)(1-¼²)……(1-1/100²)
问题描述:
(1-½²)(1-⅓²)(1-¼²)……(1-1/100²)
答
原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/99)(1+1/99))(1-1/100)(1+1/100)
=1/2 *3/2 *2/3 *4/3 *3/4* 5/4....* 98/99*100/99 * 99/100 *101/100
=1/2 * 101/100
=101/200
【俊狼猎英】团队为您解答
答
(1-½²)(1-⅓²)(1-¼²)……(1-1/100²)=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/100)(1+1/100)=1/2x3/2x2/3x4/3x3/4x5/4.x99/100x101/100=1/2x1x1.x1x101/100...