Question

先阅读第（1）小题的计算过程，再计算第（2）小题1/2+1/6+1/12+....+1/9900

（2）1/3+1/15+1/35+....+1/9999 回答好的话加分

Answer 1

（1）1/2+1/6+1/12+....+1/9900
=1/(1X2)+1/(2X3)+1/(3X4)+......+1/(99X100)
=(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
（2）1/3+1/15+1/35+....+1/9999
=(2/3+2/15+2/35+....+2/9999)/2
=[(1-1/3)+(1/3-1/5)+(1/5-1/7)+......+(1/99-1/101)]/2
=[1-1/3+1/3-1/5+1/5-1/7+......+1/99-1/101]/2
=[1-1/101]/2
=[100/101]/2
=50/101

Answer 2

(1) 原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+......+(1/99-1/100)=99/100
(2) 原式=1/2*[(1-1/3)+(1/3-1/5)+(1/5-1/7)+..........+(1/99-1/101)]
=50/101

追问

第一题错了，是99/100

Answer 3

x