1 3 ! + 2 5 ! + 3 7 ! + to is equal to

Step-by-step solution

n th term = n (2 n+1) ! = 1 2 [ (2 n+1)-1 (2 n+1) ! ]= 1 2 [ 1 (2 n) ! - 1 (2 n+1) ! ] Sum of the series aligned &= 1 2 [ 1 2 ! - 1 3 ! + 1 4 ! - 1 5 ! + 1 6 ! - 1 7 ! + ] &= 1 2 e⁻¹= 1 2 e aligned