1/52+49/52×51+49×48/52×51×50+.+49×...×1/52×...×3=?

1/52+49/52×51+49×48/52×51×50+.+49×...×1/52×...×3=
=(51*50)/(52*51*50)+(50*49)/(52*51*50)+(49*48)/(52*51*50)+.+(2*1)/(52*51*50)
=(51*50+50*49+49*48.+2*1)/52*51*50
=(1*2+2*3+3*4+.50*51)/52*51*50
其中1*2+2*3+3*4+.50*51=44200（该题计算也是采用奥数方法）
52*51*50=132600
最终结果为44200/132600=1/3

=（1/1-1/2）+（1/2-1/3）+（1/3-1/4）……+[1/n-1/(n+1)] =1/1-1/2+1/2-1/3+1/3-1/4……+1/n - 1/(n+1) =1