Question

1/2X1/3+1/3X1/4+1/4X1/5+1/5X1/6+.+1/99X1/100=?

Answer 1

1/2 X 1/3 + 1/3 X 1/4 + 1/4 X 1/5 + 1/5 X 1/6 +.+ 1/99 X 1/100

= 1/(2 X 3) + 1/(3 X 4) + 1/(4 X 5) + .+ 1/(99 X 100)

= (3 - 2)/(2 X 3) + (4 - 3)/(3 X 4) + (5 - 4)/(4 X 5) + .+ (100 - 99)/(99 X 100)

= (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) +.+ (1/99 - 1/100)

= 1/2 - 1/100 = 49/100