作业帮1/3+1/8+1/15+...+1/120=?
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/30 08:39:51
xj@_,3_zo!"Dm76+OPEWo4zdu!;3mfh
H< .N)K̦;>>:Ouۖ3(G-GbAʫy]繝 U }!'1Fm}tR)
R
Sxdu'f:Z]/J`BLI'|Y1?<2. dq{Wi111*npaE H!!} u h"FJn3 lYpDͣ #2]Y*}XOw/W^G{ˮ[qgY]d=l["*?ve
/ }@s&L^ i
ċnbX 煐NQ. `eLa|KdkxE7(3\ypјXntOU
1/3+1/8+1/15+...+1/120=?
1/3+1/8+1/15+...+1/120=?
1/3+1/8+1/15+...+1/120=?
原式＝1/(1*3)+1/(2*4)+1/(3*5)+.....+1/(10*12)=1/2[(1-1/3）+(1/2-1/4)+(1/3-1/5)+......+(1/10-1/12)]=1/2(1-1/3+1/2-1/4+1/3-1/5+........+1/10-1/12)=1/2[（1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10）-(1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12)]=1/2(1+1/2-1/11-1/12)=175/264
1/3=(1-1/3)/2
1/8=(1/2-1/4)/2
以此类推，得到上式=（1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+1/6-1/8+1/7-1/9+1/8-1/10+1/-1/11+1/10-1/12)/2=(1+1/2-1/11-1/12)/2=175/264
