Question

The sum of the first 20 terms of series 1/(5*6)+1/(6*7)+1/(7*8)+.........is

Answer 1

Answer- a¹=1/ 30 a²= 1/ 42 d= a²-a¹ so , 1/42-1/30 = 5-7/210= -1/105 here d= -1/ 105 now an= n/2(2a+(n-1)d) = 10(2×1/30+19×-1/105) = 10( 1/15+(-19/105))

= 10×7-19/105 = 10×-12/105= -24/21

hence S20= -24/21