(1/2+1/3+1/4+……+1/100)x(1+1/2+1/3+……+1/99)-(1/2+1/3+……+1/99)(1+1/2+1/3+……+1/100)
问题描述:
(1/2+1/3+1/4+……+1/100)x(1+1/2+1/3+……+1/99)-(1/2+1/3+……+1/99)(1+1/2+1/3+……+1/100)
答
(1/2+1/3+1/4+……+1/100)x(1+1/2+1/3+……+1/99)-(1/2+1/3+……+1/99)(1+1/2+1/3+……+1/100)令a=1/2+1/3+……+1/99原式=(a+1/100)(1+a)-(a)(1+a+1/100) =a+a^2+1/100+a/100-a-a^2-a/100 =1/10...