A = [tex]\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}[/tex]
1/2.3 + 1/3 .4 +1/4.5 +.... + 1/99 100
= 1/2 - 1/3 + 1/3 - 1/4 + ...+ 1/99- 1/100
= 1/2 - ( -1/3 + 1/3)+ (-1/4+1/4) + .... + (- 1/99 +1/99) - 1/100
= 1/2 - 1/100
= 1/2 - 1/100
= 50/100 - 1/100
= 49/100