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

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

1/4+1/4*7+1/7*10+........1/97*100

=1/4+1/3*(1/4-1/7+1/7-1/10+............+1/97-1/100)

=1/4+1/3*(1/4-1/100)

=1/4+1/3*(25-1)/100

=1/4+1/3*24/100

=1/4+8/100

=(25+8)/100

=33/100

1/2+1/4+1/8+1/16+……+1/1024=

1/2=1-1/2

1/4=1/2-1/4 ..... 同理 1/1024=1/512-1/1024

所以,原式=(1-1/2)+(1/2-1/4)+...+(1/512-1/1024)

=1-1/1024=1023/1024