1/(1*4)+1/(4*7)+1/(7*10)+.+1/(97*100) =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) =33/100