1/7+3/8+7/36+29/56+37/63+41/72+53/77+29/84+3/88
7/36=(3+4)/(4*9)=1/12+1/9
29/56=(21+8)/(7*8)=3/8+1/7
37/63=(28+9)/(7*9)=4/9+1/7
41/72=(32+9)/(8*9)=4/9+1/8
53/77=(42+11)/(7*11)=6/11+1/7
29/84=(36-7)/(7*12)=3/7-1/12
3/88=(11-8)/(8*11)=1/8-1/11
所以 通加就是
1/7+3/8+1/12+1/9+3/8+1/7+4/9+1/7+4/9+1/8+6/11+1/7+3/7-1/12+1/8-1/11=1+1+1+5/11=38/11
是这样的吗:
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*3）*```````*(1-1/10*10)
（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+2)+1/(1+2+3)+1/(1+2+3+4)+…+1/(1+2+3+…+49)+1/(1+2+3+…+50)
=1/[（1+2）*2/2]+1/[（1+3）*3/2]+1/[(1+4)*4/2]+……+1/[（1+50）*50/2]
=2/(2*3)+2/(3*4)+2/4*5+……+2/（100*99）
=[1/2*3+1/3*4+1/4*5+.+1/50*51]*2
=（1/2-1/3+1/3-1/4+1/4-1/5+……+1/50-1/51）*2
=(1/2-1/51)*2
=49/102*2
=49/51