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.