How to compute equation with exponents?

Question

I want to find $a$, where that term satisfies this equation:

$$a + a(1-a) + a(1-a)^2 + \cdots + a(1-a)^{15} = 0.5$$

I could write that as a sum from 0 to 15, but still it is unclear to me how should I proceed, any ideas please?

Answer 1

Hint:

$$\sum_{k=0}^{n-1} a r^k = a \frac{1-r^n}{1-r}.$$

Substitute $n=16$ and $r=1-a$.