Question

Determine if the following sequence converges or diverges: {n!/(n-2)!} n= 2, 3, 4, ... If the sequence converges, find it's limit.

Answer 1

Use ratio test! It's the best test to use when you have a sequence with factorials.

Answer 2

I really need some one to help me out and walk me through step by step please

Answer 3

Do you know the ratio test?

Answer 4

\(\large L = \lim_{n \rightarrow \infty} \left | \frac{a_{n+1}}{a_n} \right |\) IF L <1 absolutely convergent, IF L > 1 = divergent, and IF L = 1 use different test, but it generally works with factorials.

Answer 5

?? Do the individual terms approach zero (0)?

Answer 6

i know the ratio test but it isnt working out right.

Answer 7

Don't use the ratio test. This one is easier than that.

\(\dfrac{n!}{(n-2)!} = \dfrac{n(n-1)[(n-2)!]}{(n-2)!} = n(n-1)\)

Why would that converge?

Answer 8

What you're doing same thing as ratio test. The only thing is that you havent applied limits to find your radius of convergence.

Answer 9

There is no radius of convergence. There is no convergence. I did not apply a ratio test of anything like it. I simplified the expression using algebraic manipulation.