The factorial of a positive integer n, denoted n!, is equal to the product of all integers between 1 and n. That is, n! = n (n- 1) (n - 2) .. (2) · (1). For example, 1! = 1, 2! = 2 ·1 = 2, 3! = 3- 2 1= 6, 4! = 4 . 3· 2. 1 = 24, etc. As a result, one can show that n! 2 n for all n 2 4 (try calculating n! and n for a few values of n 2 4 to convince 1 converges or diverges. n! n=1 yourself of this). Use this and the Comparison Test to determine whether O a. The series converges. O b. The series diverges. iM:

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