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

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/24 01:14:51
1/52+49/52×51+49×48/52×51×50+.+49×...×1/52×...×3=?
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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=?

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