The value of 2 1 ! + 2 + 4 2 ! + 2 + 4 + 6 3 ! + … . is

Step-by-step solution

Here, T n = n ( n + 1 ) n ! = n - 1 + 2 ( n - 1 ) ! = 1 ( n - 2 ) ! + 2 ( n - 1 ) ! ∴   S = ∑ n = 1 ∞ T n = ∑ n = 1 ∞ 1 ( n - 2 ) ! + 2 ∑ n = 1 ∞ 1 ( n - 1 ) ! = e + 2 e = 3 e