Question

\[a_n =\frac{n!}{2^n}\]

Answer 1

ratio test?

Answer 2

\(\sum a_n\)?

Answer 3

ratio test would work nicely, as you would have an avalanche of cancellation

Answer 4

determine whether the sequence converges or diverges. if it converges, find the limit

Answer 5

oh sequence, no series

Answer 6

I'm going back to the first section of the chapter...trying to remember how I solved it

Answer 7

\[lim_{n\rightarrow\infty}\]?

Answer 8

is infinite

Answer 9

let's see, how do I show this mathematically again?

Answer 10

you could probably write down exactly what it is
\[\frac{1\times 2\times 3\times 4\times ...\times n}{2\times 2\times 2\times 2\times ...\times 2}\]

Answer 11

then maybe start at 3 and write
\[\geq \frac{1}{2}\times \frac{3^{n-2}}{2^{n-2}}\]
\[=\frac{1}{2}(\frac{3}{2})^{n-2}\] which pretty clearly goes to infinity since \(\frac{3}{2}>1\)

Answer 12

oh perfect

Answer 13

why n-2

Answer 14

doesn't really matter because n goes to infinity, but i wrote \(n-2\) since i cut off the first two terms

Answer 15

I see

Answer 16

well thanks again Satellite!

Answer 17

yw