The Gauss' Trick

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Overview

A method for finding the sum of an arithmetic series in O(1) time.

S = (n / 2) * (i + j);

Where:

i: First term.
j: Last term.
n: Number of terms.
```
n = (j - i) / d + 1;
```
- d: Common difference (the step between terms).
  - e.g., in 2, 4, 6, 8 the step is 2, so d = 2.

i = 0
j = 10
d = 1
n = (10 - 0) / 1 + 1 = 11

S = (11 / 2) * (0 + 10) = 5.5 * 10 = 55

i = -5
j = 2
d = 1
n = (2 - (-5)) / 1 + 1 = 8

S = (8 / 2) * ((-5) + 2) = 4 * (-3) = -12

i = 2
j = 14
d = 2
n = (14 - 2) / 2 + 1 = 7

S = (7 / 2) * (2 + 14) = 3.5 * 16 = 56

⌘I