Question

2分之1 + 6分之5 + 12分之11 +20分之19 +.+ 99×100 分之9899 求简算

Answer 1

1/2 + 5/6 + 11/12 + 19/20 +.+ 9899/99×100

=(1-1/2)+(1-5/6)+(1-11/12)+(1-19/20)+.+(1-9899/9900)

=99-(1/2+1/6+1/12+1/20+.+1/9900)

=99-[(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+.+(1/99-1/100)]

=99-(1-1/100)

=99-99/100

=9801/100

打字不易,不明白追问哦!