1234567
of 7

Gauss's Problem and Arithmetic Series

Let's write out the problem like this:

1 + 2 + 3 + 4 + ... + 50 + 51 + ... + 97 + 98 + 99 + 100

There's a pattern here!

Check this out:

1 + 2 + 3 + 4 + ... + 50 + 51 + ... + 97 + 98 + 99 + 100 ... 1 and 100 add up to 101 ... 2 and 99 add up to 101 ... 3 and 98 add up to 101 ... 4 and 97 add up to 101 ... 50 and 51 add up to 101

There are 50 pairs of 101...

That's50( 101 ) = 5050

Dang!
 

TRY IT:

Find the sum of the integers from 1 to 40.

 

Find the sum of the integers from 1 to 62.