_ n=1 ^ 2 n (2 n+1) ! is equal to

Step-by-step solution

aligned & _ n=1 ^ 2 n (2 n+1) ! = _ n=1 ^ 2 n+1-1 (2 n+1) ! &= _ n=1 ^ ( 1 2 n ! - 1 (2 n+1) ! ) &= ( 1 2 ! - 1 3 ! )+ ( 1 4 ! - 1 5 ! )+ &=1- 1 1 ! + 1 2 ! - 1 3 ! + 1 4 ! - 1 5 ! + &=e⁻¹= 1 e aligned