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=1-1/2
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