SOLUTION: A recursive formula for the following series: 1, 3/2, 5/6, 7/24, 9/120

Question 871381: A recursive formula for the following series: 1, 3/2, 5/6, 7/24, 9/120
Found 2 solutions by KMST, richwmiller:
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
A recursive formula shows how to get the next term from the one before, to from .
I know the idea to get from .
From the terms you are given, in the form given,
to get term number ,
you add 2 to the numerator and multiply the denominator by .
So for the 6th term, you take ;
change the numerator from to ,
and change the denominator from to ,
to get .

However, if I was given as a term, how would I know that ,
and how would I know that is the fifth term.
It is not so easy.
I could do it, but I do not know how to write it as a recursive formula..

I do see an explicit formula to calculate term number from , not counting on term number ) .

If you only told me that one of the terms is ,
I would factor as .
I would multiply numerator and denominator times ,
to have as a denominator.
Then, suspecting that is term number ,
I would verify that with as denominator, the numerator is .
After that, from ,
I would change the numerator from to ,
and change the denominator from to ,
to get .
I cannot write that as a recursive formula,
but since no one else answered your question before,
I assume that not many people can.

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
(n+2)/d!*(d+1))
where n is last numerator
and d! is last denominator

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