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Brilliant! Thanks to both bobbym and gAr!
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!
Im trying to find an expression for the limit below. I know a limit exists because I can calculate it in Excel but Id 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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