Show that $\sum_{k=1}^{n} c^k = \frac{c(c^n-1)}{c-1}$?

Question

How would one show that the summation $\sum_{k=1}^{n} c^k = \frac{c(c^n-1)}{c-1}$ is true?

Answer 1

Guide:

Suppose $$S = \sum_{k=1}^n c^k \tag{1}$$

$$cS = \sum_{k=1}^n c^{k+1}\tag{2}$$

Use the second expression to subtract the first expression and then solve for $S$.