Name for inequality about sums of exponents with same base

Question

Is there a name for the following inequality regarding sums of exponents which share a base?

$$\text{For all integers $b \geq 2$, $n \geq 1$,} \\ \sum_{i=0}^{n-1}{b^i} < b^n$$

Answer 1

I doubt it has a name, since the proof is so straightforward.

$$\sum_{i=0}^{n-1}{b^i} = \frac{b^n-1}{b-1} \le b^n-1 < b^n$$

The key part is the equality, which is called a geometric series or the sum of a geometric progression. The inequalities are consequences of your restrictions on $b$ and $n$.