Monotone convergence theorem

The monotone convergence theorem is like counting blocks. You know how sometimes you might have a big pile of blocks and you want to know how many there are, but you don't want to count them one by one? That's where the monotone convergence theorem comes in.

Imagine you have a pile of blocks that keeps getting bigger and bigger, but the blocks are all the same size. If you put the blocks in a line and count them one by one, you would be counting forever! But, if you know that the pile is always getting bigger, you can start at the bottom and keep adding up the blocks as you go. As you add more and more blocks, you get closer and closer to the total number of blocks in the pile.

The monotone convergence theorem is like this. It says that if you have a sequence of numbers (like the number of blocks in a pile), and the sequence keeps getting bigger or smaller (monotone), then you can add up all the numbers in the sequence (like counting the blocks) and you will get closer and closer to a certain number (the limit).

So, just like counting blocks, you can use the monotone convergence theorem to figure out the total value of a sequence of numbers without having to add them up one by one. Pretty cool, huh?