How Does Convergence and Divergence: The Return of Sequences and Series Work?

A sequence is just a list of numbers that follow a pattern, think of it like counting stairs one by one as you go up.

When we talk about convergence, imagine you're trying to reach the top of a slide. Each time, you get closer and closer to the top. If you keep going, eventually, you’ll be right at the very top, that’s convergence! In math terms, if the numbers in your list get closer and closer to a certain value, we say the sequence converges to that value.

Now think about when you're bouncing on a trampoline. Each time you jump, you go higher and higher, that’s divergence! If the numbers in your list keep growing or keep moving away from any fixed point, we say the sequence diverges.

A series is like adding all those stairs together. If the total keeps getting bigger and bigger, like you're stacking blocks higher and higher, that's divergence again. But if it settles down to a certain number, like your piggy bank filling up just right, that’s convergence! A sequence is just a list of numbers that follow a pattern, think of it like counting stairs one by one as you go up.

Now think about when you're bouncing on a trampoline. Each time you jump, you go higher and higher, that’s divergence! If the numbers in your list keep growing or keep moving away from any fixed point, we say the sequence diverges.

A series is like adding all those stairs together. If the total keeps getting bigger and bigger, like you're stacking blocks higher and higher, that's divergence again. But if it settles down to a certain number, like your piggy bank filling up just right, that’s convergence!