Question

summation (3^n)( n!)/(n^n)
does the above series converge or diverge when n goes to infinity?

Answer 1

Use Ratio test

Answer 2

or Root test

Answer 3

i know that but i m getting it to be convergent when it is a divergent series

Answer 4

ya it is divergent the limit is 3e^(-1) which is larger than 1

Answer 5

how did u get e?

Answer 6

Ratio test

lim |a_(n+1)/a_n|
= lim 3[n/(n+1)]^n

Answer 7

o yea... so n/n+1)^n = e right

Answer 8

sorry 1/e

Answer 9

yup, the limit is 1/e

Answer 10

Do you know how to get that limit?