Question

Find the closed form of the sum

Answer 1

\[\sum_{i=j}^{n}\frac{u^id^{n-i}n!}{(n-i)!*i!}p^i(1-p)^{n-i}\]

Answer 2

\[\sum_{i=0}^{n}f(i,n)* \binom{n}{i}p^i(1-p)^{n-i}\]Where f(i,n) = 0 for all\[i \le j = \frac{ln(\frac{K}{d^nS_0})}{ln(\frac{u}{d})}\]Where K, d, u, and S_0 are constants

Answer 3

http://www.wolframalpha.com/input/?i=%5Csum_%7Bi%3Dj%7D%5E%7Bn%7D%5Cfrac%7Bu%5Eid%5E%7Bn-i%7Dn!%7D%7B(n-i)!*i!%7Dp%5Ei(1-p)%5E%7Bn-i%7D

hypergeometric function! good luck with that :P

but if i starts from 1,
http://www.wolframalpha.com/input/?i=%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%5Cfrac%7Bu%5Eid%5E%7Bn-i%7Dn!%7D%7B(n-i)!*i!%7Dp%5Ei(1-p)%5E%7Bn-i%7D

Answer 4

So my professor was initially asking for the closed form formula, but then she said write down a formula in terms of only these parameters so that you can plug them in and get the result. (u,d,r,s,K and n)

Answer 5

and if i starts from 0, as parth said, its just
\((pu-d(p-1))^n\)