1/(3×5)+1/(5×7)+1/(7×9)+...+1/(97×99)
=1/2*(1/3-1/5)+1/2*(1/5-1/7)+1/2*(1/7-1/9)+...+1/2*(1/97-1/99)
=1/2*(1/3-1/5+1/5-1/7+1/7-1/9+...+1/97-1/99)
=1/2*(1/3-1/99)
=1/2*32/99
=16/99
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)
=1/3*99/100
=33/100