1 + 2 + 3 + 4 + ···

Imagine you have a bunch of toys to count. First, you have one toy. Then you get two more toys. Now you have three toys in total. Next, you add three more toys. Now you have six toys. Then you add four more toys, which makes a total of ten toys. You keep adding more and more toys this way, each time the amount you add increasing by one. This goes on forever and ever. But even though you keep adding more and more toys, you can always figure out how many toys you have by adding them up. This is what we call adding numbers together in a sequence. The sequence in this case is 1, 2, 3, 4, 5, and so on. So when we add up 1 + 2 + 3 + 4 + ···, we are adding up all the numbers in this sequence. The answer to this problem is actually infinity, which means the number just keeps getting bigger and bigger without ever stopping. But don't worry, we don't need to count that high to understand what's happening in this problem. We just need to know that we're adding up a bunch of numbers that go on forever.