Which of the following series is convergent

Question

#2 Which of the following series is convergent choice 1, choice 2, choice 3, choice 1 & 2, all choices: (WAITING)

1) 1 is the lower limit ∞ is the upper limit function is (8^n)/(n!),   

 2) 1 is the lower limit ∞ is the upper limit function is (n!)/(n^100), 

 3) 1 is the lower limit ∞ is the upper limit function is (n+1)/(n)(n+2)(n+3)     

Answer 1

1...converges by the ratio test.

2...diverges because the sequence does not converge (for large n, n!>n¹⁰⁰).

3...converges because for all n, the terms are less than 1/n² which converges.