1/4+1/28+1/70.+1/9700

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1/4+1/28+1/70.+1/9700
1/4+1/28+1/70.+1/9700

1/4+1/28+1/70.+1/9700
=1/1*4+1/4*7+1/7*10+……+1/97*100
=(1/3)*(1-1/4)+(1/3)*(1/4-1/7)+(1/3)*(1/7-1/10)+……+(1/3)*(1/97-1/100)
=(1/3)*(1-1/4+1/4-1/7+1/7-1/10+……+1/97-1/100)
=(1/3)*(1-1/100)
=33/100

1/4+1/28+1/70......+1/9700
=(1/3)*(1-1/4+1/4-1/7+1/7-1/10+...+1/97-1/100)
=(1/3)*99/100
=33/100

原式=1|4+1|4*7+1|7*10+......1|97*100(共有(100-1)|3=33个数)
=33|(33*3+1)=33|100