Solving the summation of a geometric series

Question

Lets assume we have the following summation... and we are asked to evaluate the summation

$$\sum_{i=0}^{\log (n)} (4^i)$$

I know that this is a geometric series and it converges if 4 is less than one. Obviously this is false, therefore the summation cannot converge to a single value. Therefore the result is infinity

Is this the proper approach to solving the summation. Did i even get the correct answer?

Answer 1

Notice that this is a finite sum.

The following formula might help you, if $m \in \mathbb{N}$,

$$\sum_{k=0}^{m-1}ar^k=a\left(\frac{1-r^m}{1-r} \right)$$

Answer 2

For any $n$, this is a sum of a finite number of terms, so the sum is finite.

Just use the standard formula for the sum of a geometric series and put in 4 as the ratio and log n and 0 as the upper and lower limits.