I have function $f$, where $f^n$ denotes composition and $0<k<1$. I need to write the following in summation notation:
$$f^0(k^n)+f(k^{n+1})+f^2(k^{n+2})+f^3(k^{n+3})+\dots +f^{n+p-1}(k^{n+p-1}) $$
I should be able to write something like this?
$$\sum_{i=0}^{n+p-1}f^i(k^{?})$$
If the last term is instead supposed to be $f^{p-1}(k^{n+p-1})$, then the sum is $$\sum_{i=0}^{p-1}f^i(k^{n+i}).$$ Otherwise, you need to explain the pattern.
In summation notation it should be \begin{equation} \sum_{i=0}^{n+p-1}f^i(k^{n+i}).\end{equation}
So the exponent of $k$ in the last term should be $2n+p-1$.
