4分之1+28分之1+70分之1+……+9700分之1=

题目

4分之1+28分之1+70分之1+……+9700分之1=
快啊,就要上学了……回答了全部的分都送……回答对了,

答案

1/4+1/28+1/70+...+1/9700
=1/(1*4)+1/(4*7)+1/(7*10)+...1/(97*100)
=1/3(1/1-1/4)+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)
=1/3*(99/100)
=33/100
[公式:1/(a*b) (b>a)
=[1/(b-a)] *(1/a-1/b) ]