Gauss Trick (Summing up a series of number )

Problem

Summing up a series of number <MATH> 1 + 2 + \dots + 50 + 51 + \dots + 99 + 100 </MATH>

Solution

There is a pattern, there is 50 pairs of value 101:

• <math>1 + 100</math>
• <math>2 + 99</math>
• …
• <math>50 + 51</math>

The total is then <MATH> 50 * 101 = 5050 </MATH>