The Gauss' Trick

Documentation Index

Fetch the complete documentation index at: https://mintlify.com/sh2aliyev/notes/llms.txt

Use this file to discover all available pages before exploring further.

​

Overview

​

Formula

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

• 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.

​

Examples

​

1. Sum of numbers from 0 to 10

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

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

​

2. Sum of numbers from -5 to 2

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

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

​

3. Sum of the numbers [2, 4, 6, 8, 10, 12, 14]

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

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