Question About Notation of CRR I am reading a book on financial theory and it has been a while since I took a notation heavy math course so could someone help me out here...

Now with this equation how does the sum work? Do I do the factorials first? Is it a sum for each value from 0 to i? Is everything to the right of the sum sign included each iteration of the sum?
thanks!
 A: In this particular case, yes, everything to the right of the summation sign is included in each iteration of the sum.
It is a sum for each value of i from 0 to N.
If you wanted to evaluate this at some value, you would do the summation first, and then begin to expand the resulting expression.
For example, consider the simpler expression
$$(1 + n^2)\sum\limits_{i = 1}^n i + 2.$$
evaluated at $n = 4$, say.
The first step to take would be to substitute in $4$ for $n$, giving
$$(1 + 4^2)\sum\limits_{i = 1}^4 i + 2.$$
Then, expand the summation, giving
$$\begin{align}
(1 + 4^2)((1 + 2) + (2 + 2) + (3 + 2) + (4 + 2)) &= (1 + 16)(3 + 4 + 5 + 6)\\
&= (17)(18)\\
&= 306.
\end{align}$$
Essentially, the summation is expanded first, then the interior of the summation is evaluated, and then that result gets combined with the outside.
You can think of a summation as implying parentheses, with the left paren just to the left of the $\sum$, and the right paren at the far end of the expression being summed over.
