Using a telescoping sum express the sum of the series Please

Using a telescoping sum, express the sum of the series. Please explain step-by-step so I can learn for future problems.

Solution

we can break the term as [(n+3)-(n+1)]/[(n+3)(n+1)] term is =>1/(n+1) - 1/(n+3) putting in terms from n=1 to infinity {1/2+1/3+1/4......0]- [1/4+1/5...........0] => 1/2+1/3 [ since all other terms cancel out] =5/6 answer