I am having problem with this question. Please help

Find showing all working, a recursive definition of the sequence with general term

from n1 onwards

How am I suppose to find the recursive definition? What are the steps?

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- Mar 21st 2013, 11:21 PMNewbie999Sequence with factorial
I am having problem with this question. Please help

Find showing all working, a recursive definition of the sequence with general term

from n1 onwards

How am I suppose to find the recursive definition? What are the steps? - Mar 21st 2013, 11:58 PMMacstersUndeadRe: Sequence with factorial
A recursive definition requires two components

1) A (a base term)

2) A general formula relating and for where n is a natural number

--

Finding is easy. Replace to get

Since we know the formula for we also know the formula for (replace n with n+1)

Now consider , the ratio between two consecutive terms, and isolate for the recursive formula as desired. I'll leave the rest to you. - Mar 22nd 2013, 12:14 AMNewbie999Re: Sequence with factorial
Macsters thank you very much for the reply.

I don't think I came up with the right answer and I can't simply anymore because my algebra is very bad.

Simplified

I am a bit lost from this point. Can you please tell me if I am even on the right track? - Mar 22nd 2013, 12:25 AMMacstersUndeadRe: Sequence with factorial
- Mar 22nd 2013, 12:27 AMNewbie999Re: Sequence with factorial
Thank you sooo much : ) for everything.

Edit: One more question. I would like to send you a PM since this is solved but someone might found it useful to see the question here.

With the

I pretty much understand everything above and the final answer.

But what if

How can I calculate a sequence when it's relating to previous number? Lets say n-1 or n-2. - Mar 22nd 2013, 10:00 AMMacstersUndeadRe: Sequence with factorial
If the general formula for was instead, then

hence

so this is still a relationship between two consecutive numbers. Replace n with n-1 and you get a relationship between and - Mar 31st 2013, 12:31 AMvicwilson123Re: Sequence with factorial
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