What is the sum of the first 2020 positive integers?

Question

How do you get the sum of the first 2020 positive integers?

Can you show me the math to find it too.

Answer 1

I assume you don't want to write down all the numbers, or use a calculator, and add them 1 at a time.

There's a trick. Consider adding 1 + 2020 = 2021

2 + 2019 = 2021

3 + 2018 = 2021

This can be continued until you reach

1010 + 1011 = 2021

So there are 1010 pairs of numbers adding up to 2021, and therefore the total will be 1010 X 2021 = 2,041,210

This works in general, for the sum of numbers 1 to n, the answer will be n(n + 1)/2. In this case,

n was 1010. It even works when n is an odd number, because you can add the first n - 1 numbers first, and then add n. he formula would work, since (n - 1)n/2 + n = [(n - 1)n + 2n]/2 = (n - 1 + 2)n/2 = (n + 1)n/2, which will be the same as n(n + 1)/2.