I have a series that I have discovered within a recurrence relation and want to convert this into an equation to finish unfolding the relation. How can I convert a summation like this to a simple equation?
$$\sum_{i=1}^n 100(4^{i-1})$$ For all $n\geq1$.
It's a sum of the geometric progression.
$$\sum_{i=1}^n 100(4^{i-1})=100\cdot\frac{4^n-1}{4-1}$$