The sum of the first 20 terms of the series

$\frac{1}{5 \times 6} + \frac{1}{6 \times 7}+\frac{1}{7 \times 8}+....$ is

A) 0.16

B) 1.6

C) 16

D) None of these


Option A


The series is $\sum_1^\infty\frac{1}{(n+4)(n+5)}$ ;n = 1,2,3,4...20
we can write the above as:


20th term is

Then the sum of 20 terms of series is
cancel the plus minus we get as the below:
= 0.16