Sum the following series to n terms and to infinity :
(i) `(1)/(1.4.7) + (1)/(4.7.10) + (1)/(7.10.13) + ...` (ii) `sum_(r=1)^(n) r (r + 1) (r + 2) (r + 3)` (iii) `sum_(r=1)^(n) (1)/(4r^(2) - 1)`

Answer

(i) `s_(n) = (1//24) - [1//{6(3n + 1)(3n + 4)}]; s_(oo) = 1//24` (ii) `(1//5) n (n + 1) (n + 2) (n + 3) (n + 4)` (iii) `n//(2n + 1)`