1/7+3/8+7/36+29/56+37/63+41/72+53/77+29/84+3/88====39*148/149+148*149/86+48*14/149====（1-1/2*2）*（1-1/3*3）*```````*(1-1/10*10)====1/1+2 + 1/1+2+3 + 1/1+2+3+4 + ```````1/1+2+3+````+50====要清楚 这有点难度 所以 欧也!

(1 / 7) + (3 / 8) + (7 / 36) + (29 / 56) + (37 / 63) + (41 / 72) + (53 / 77) + (29 / 84) + (3 / 88)
=1/7+3/8+(3/4-5/9)+(1/7+3/8)+(1/7+4/9)+(1/8+4/9)+(1/7+6/11)+(3/7-1/12)+(1/8-1/11)
=(1/7+1/7+1/7+3/7+1/7)+(3/8+3/8+1/8+1/8)+(4/9+4/9-5/9)+3/4-1/12+(6/11-1/11)
=1+1+(3/9+3/4-1/12)+5/11
=3又11分之5
39*148/149+148*86/149+48*74/149
=(39*148+86*148+24*2*74）/149
=(39+86+24)*148/149
=149*148/149
=148
（1-1/2^2）（1-1/3^2）…（1-1/10^2）
因为:1-1/2^=(1-1/2)(1+1/2)=1/2*3/2
1-1/3^=(1-1/3)(1+1/3)=2/3*4/3
所以原式=1/2*3/2*2/3*4/3…………9/10*11/10
=1/2*11/10
=11/20
1/(1+2+…+n)=1/〔(1+n)n÷2〕＝2/(1+n)n＝2×[1/n－1/(n+1)]
1/(1+2)＋1/(1+2+3)＋1/(1+2+3+4)＋……＋1/(1+2+3+……+10)
＝2×(1/2－1/3)＋2×(1/3－1/4)＋2×(1/4－1/5)＋……＋＋2×(1/10－1/11)
＝2×（1/2－1/3＋1/3－1/4＋1/4－1/5＋……＋1/10－1/11）
＝2×（1/2－1/11）
＝9/11

（1-1/2*2）*（1-1/3*3）*```````*(1-1/10*10)
=(1-1)*(1-1)*……*（1-1）
=0

1/7+3/8+7/36+29/56+37/63+41/72+53/77+29/84+3/887/36=(3+4)/(4*9)=1/12+1/929/56=(21+8)/(7*8)=3/8+1/737/63=(28+9)/(7*9)=4/9+1/741/72=(32+9)/(8*9)=4/9+1/853/77=(42+11)/(7*11)=6/11+1/729/84=(36-7)/(7*12)=3...

1/7+3/8+7/36+29/56+37/63+41/72+53/77+29/84+3/88
=1/7+3/8+(3/4-5/9)+(1/7+3/8)+(1/7+4/9)+(1/8+4/9)+(1/7+6/11)+(3/7-1/12)+(1/8-1/11)
=(1/7+1/7+1/7+3/7+1/7)+(3/8+3/8+1/8+1/8)+(4/9+4/9-5/9)+3/4-1/12+(6/11-1/11)
=1+1+(3/9+3/4-1/12)+5/11
=3又5/11
39*148/149+148*149/86+48*14/149(题目有误)
39*148/149+148*86/149+48*74/149
=(39*148+86*148+24*2*74）/149
=(39+86+24)*148/149
=149*148/149
=148
（1-1/2^2）=(1-1/2)(1+1/2)=1/2*3/2
（1-1/3^2）=(1-1/3)(1+1/3)=2/3*4/3
...
（1-1/9^2）=8/9*10/9
（1-1/10^2）=9/10*11/10
（1-1/2^2）（1-1/3^2）（1-1/4^2）...（1-1/9^2）（1-1/10^2）
=1/2*3/2*2/3*4/3*...*8/9*10/9*9/10*11/10
=1/2*11/10
=11/20
1+1/[(1+2)*2/2]+1/[(1+3)*3/2]+.....+1/[(1+50)*50/2]
=1+2/(2*3)+2/(3*4)+2/(4*5)+.........+2/(50*51)
=1+2(1/2*3+1/3*4+1/4*5+.....+1/50*51)
=1+2(1/2-1/3+1/3-1/4+1/4-1/5+.....+1/50-1/51)
=1+2(1/2-1/51)
=1+49/51
=1又49/51
=100/51