How would you deal with a factorial in a ratio test to find the lim n→∞ .
here is the question:
∞ ∑ 1 / (2n+1)! 0
Un = 1 / (2n+1)!
Un+1 = 1 / (2n+3)!
(Un)/(Un+1)= 1 / (2n+3)! . (2n+1)! / 1
(Un)/(Un+1)= (2n+1)! / (2n+3)!
note that (2n + 3)! = (2n + 3)(2n + 2)(2n + 1)!
so (2n+1)! / (2n+3)! = (2n + 1)! / (2n + 3)(2n + 2)(2n + 1)! the (2n + 1)!'s cancel leaving 1/(2n + 1)(2n + 2), this goes to zero as n goes to infinity
What does the infinity on top of the sum sign and the zero below the sum sign mean? As I have seen some questions with n=1 instead of the zero? Thanks
∞
∑
0
What does the infinity on top of the sum sign and the zero below the sum sign mean? As I have seen some questions with n=1 instead of the zero? Thanks
∞
∑
0
The infinity on top means it is an infinite sum, that is the limit.