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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.