Question

does An = (n!)/n converge? if so determine the limit and justify your answer with theorems. Please help

Answer 1

The sequence or the sum?

Answer 2

sequence my bad

Answer 3

no, it goes to infinity.... as n gets larger only the last n is cancelled out by the n in the denominator. it's equal to An = (n-1)!, which also goes to infinity.

Answer 4

ok is there any theorem that describes that or is just from analyzing the sequence?

Answer 5

just analyzing the sequence. n! is equal to n * n-1 * n-2 .... 1. Dividing by n just cancels out the n term in the numerator, leaving everything from n-1 down to 1. So An = n!/n is equal to An = (n-1)!, which clearly goes to infinity.

Answer 6

ok thanks so much