Ratio Test for Convergence

So out of all my work all of this is correct except the denominator. I tried everything. When I put in (2n+2)! my online assignment says cancel out further and to simplify. WHAT???

I hate convergence/divergence. You all will soon learn that from my next several posts haha

Thank you to anyone that can help!(Clapping)

Re: Ratio Test for Convergence

you better have a look here first and then show us some of your work...

Ratio test - Wikipedia, the free encyclopedia

Re: Ratio Test for Convergence

This looks fairly straightforward to me but it is impossible to suggest where you might have made a mistake without seeing what **you** did! You know, of course, that $\displaystyle a_n= \frac{9^n}{(2n)!}$. So what is $\displaystyle a_{n+1}$? What is $\displaystyle \frac{a_{n+1}}{a_n}$? What can you cancel?

Re: Ratio Test for Convergence

Quote:

Originally Posted by

**cld1126** So out of all my work all of this is correct except the denominator. I tried everything. When I put in (2n+2)! my online assignment says cancel out further and to simplify. WHAT???

OK, so here's something that can actually be addressed. The more working out you show us, the more guidance we are able to give you.

Notice that (2n + 2)! = (2n + 2)(2n + 1)(2n)!

Can you see how the (2n)! will cancel?

Re: Ratio Test for Convergence

Quote:

Originally Posted by

**Prove It** OK, so here's something that can actually be addressed. The more working out you show us, the more guidance we are able to give you.

Notice that (2n + 2)! = (2n + 2)(2n + 1)(2n)!

Can you see how the (2n)! will cancel?

Thank you so much, yes that makes perfect sense now. I was using the factorial incorrectly. My textbook gives a lot of proofs with almost no application or examples. The answer they were looking for was (2n+2)(2n+1). Thank you again.