00:01
In this question, we are asked to find the sum if a geometric series converges.
00:10
Converges means it would add to a non -infinite amount, so we can determine the actual number.
00:18
In order to figure out if a series converges or diverges, though, we need to determine the ratio.
00:26
If it converges, we can use this equation.
00:30
The sum of a geometric series is equal to a sub 1 or the first term in that series over 1 minus that ratio.
00:41
How do we know what the ratio needs to be, though, for it to converge? if the absolute value of my ratio is less than 1, my series converges.
00:58
Let's look at what the ratio is in this problem.
01:03
Our first two terms are 2 over 5 to the 4th, 2 to the 4th over 5 to the 5th...