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#1 Re: Help Me ! » Limit of Quotient of Infinite Series » 2011-06-03 11:29:05

Brilliant!  Thanks to both bobbym and gAr!

#2 Re: Help Me ! » Limit of Quotient of Infinite Series » 2011-06-02 09:07:56

Yes, indeed!  Well done.  This is already a huge simplification that can help me quickly approximate the limit using high values of n.  That's 99% of what I was looking for.

Just curious, can you point me to some reference material for how you came to these expressions?  Especially the one for the numerator.

Thx!

#3 Help Me ! » Limit of Quotient of Infinite Series » 2011-06-02 06:21:56

jhomme
Replies: 7

I’m trying to find an expression for the limit below.  I know a limit exists because I can calculate it in Excel but I’d like to find a closed-form version.  Any ideas on how to evaluate this?

a: = sum of (1+g)^(i-1) * (1-p)^(n-i), where i=1..n
b:= sum of (1+g)^(i-1), where i=1..n

evaluate limit as n-->infinity of {a/b}

Assume that p and g are constants such that:
0<p<1
-1<g<1


The quotient is essentially a weighted average where the weight factor is (1-p)^(n-i).  Larger values of i will have greater weight in the average.

Thanks!

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