Question

1/6, 1/4, 1/3 find the 20 th term

Answer 1

Answer:

The series is

∑1/(n+4)(n+5) where n=1,2,3,…,20

We can rewrite the series as in the form

∑ {1/(n+4) - 1/(n+5)} , 20th term is 1/20+4 - 1/20+5 => 1/24 - 1/25

then the sum of first 20 terms of the series is

1/5 - 1/6 + 1/6 - 1/7 + 1/8 - 1/9 + 1/9 - 1/10 + … + 1/24 - 1/25

= 1/5 - 1/25 = 25–5 / 25*5 = 20 / 25*5 = 4/25