The sum from 1 to n

The sum of all integers from $1$ to $100$ can be calculated by a clever method. We divide all the numbers into pairs: $1$ and $100$, $2$ and $99$, $3$ and $98$, and so on. The sum of each pair is $101$. The number of such pairs is 100/2 = 50. Therefore, the sum equals (1 + 100) \times 100 / 2. The same formula works for an odd number of terms; for example: 1 + 2 + 3 = (1 + 3) \times 3 / 2 = 6.