1/(1*2)+1/(1*2*3)+1/(1*2*3*4)+……+1/(1*2*3*4*……*100)99/100_数学解答

1/(1*2)+1/(1*2*3)+1/(1*2*3*4)+……+1/(1*2*3*4*……*100)
99/100

人气：245 ℃　时间：2020-05-08 10:52:56

解答

1/(1*2)+1/(1*2*3)+1/(1*2*3*4)+……+1/(1*2*3*4*……*100)
=（1-1/2）+（1/2-1/3）+（1/3-1/4）+……+（1/99-1/100）
=1-1/2+1/2-1/3+1/3-1/4+……+1/99-1/100
=1-1/100
=99/100