Simplification of a series

Question

I have a series in the following form:

\begin{equation} \sum_{k=1}^{n} A\exp(\mu t(k-1)+\sigma \sqrt{t(k-1)}) \end{equation}

I would like to know if I can convert this equation with something such as a geometric series, given that I see some similarities to that:$\sum _{k=1}^{n}ar^{k-1}={\frac {a(1-r^{n})}{1-r}}$, I might be completly wrong of course.

Answer 1

1. $\exp(\mu kt) \ne \exp(\mu t) \exp(k-1)$

2. Your $C$ depends on $k$. So your series has nothing to do with a geometric series.

Answer 2

Unfortunately almost all series are not simplifiable. But if you are doing applied math in finance, you could use a lot of approximation methods and numerical methods to acquire desired results. However, in order to determine which approximation methods is legit, one must know the background of your questions, so one will not omit important details while doing simplification.