For the sequence, find a formula for the general term and specify the appropriate starting value of n.
If we look at the denominator first we see the sequence (2n)!, starting at n = 1. Taking signs into account, the general term is
If we look at the signs first we might see the sequence (-1)n starting at n = 0. Then the general term is
Be Careful: When dealing with factorials, be careful with your parentheses. In particular,
(2n)! ≠ 2n!
For example, if n = 4 then
(2n)! = 8! = 40320
2n! = 2(4!) = 42.