Closed formula for sum of increasing exponents

Question

I have a sum of the form c¹+c²+...cⁿ. Is it possible to obtain a closed formula for this, and if so how?

Answer 1

You're probably looking for Faulhaber's formula.

Revised answer after question edit: What you've written is the sum of a geometric sequence. A closed form of the sum is: $$\sum_{k=1}^n C^k=\frac{C(C^n - 1)}{C-1}$$