Question

1.一乘四分之一加四乘七分之一加七乘十分之一加十乘十三分之一加……加九十七乘一百分之一

Answer 1

1、

=(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)

=33/10

2、

=1/2*(1/1*2-1/2*3)+1/2*(1/2*3-1/3*4)+1/2*(1/3*4-1/4*5)+1/2*(1/4*5-1/5*6)+1/2*(1/5*6-1/6*7)

=1/2*(1/1*2-1/6*7)

=5/21

3、

=1/2*(1-1/3)+1/2*(1/3-1/5)+……+1/2*(1/13-1/15)

=1/2*(1-1/3+1/3-1/5+……+1/13-1/15)

=1/2*(1-1/15)

=7/15