Ratio test

The ratio test is like when you are trying to figure out how much of one thing you need compared to another thing. Let's say you want to make lemonade, and you need to figure out how much water to put in compared to how much lemon juice.

You mix one cup of lemon juice with five cups of water, and it tastes just right. But what if you want to make more lemonade? You can use the ratio test to figure out how much water to add based on how much lemon juice you have.

You take the amount of lemon juice you have, and divide it by the amount of lemon juice you started with (one cup). Let's say you have two cups of lemon juice. You divide 2 by 1, and get 2.

Then you take the amount of water you used (five cups), and multiply it by the number you got (2). So 5 times 2 is 10.

So for two cups of lemon juice, you need 10 cups of water. This is like the ratio test because you are comparing the amount of one thing (lemon juice) to the amount of another thing (water) to figure out how much of each you need.

In math, the ratio test is used to figure out if a series (a bunch of numbers added together) is getting bigger or smaller as you add more numbers. Just like with the lemonade, you compare how much each number is changing compared to the previous number. If the amounts are getting smaller, the series will converge (come together to one number), and if they are getting bigger, the series will diverge (go off to infinity).