Question

List of formulas of number system

Answer 1

Important Formulas of Number System

1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2

(1² + 2² + 3² + ….. + n²) = n ( n + 1 ) (2n + 1)/6

(1³ + 2³ + 3³ + ….. + n³) = (n(n + 1)/2)²

Entirety of first n odd numbers = n²

Entirety of first n even numbers = (n + 1)

Mathematical Formulas

1. (a + b)(a – b) = (a² – b²)

2. (a + b)² = (a² + b² + 2ab)

3. (a – b)² = (a² + b² – 2ab)

4. (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

5. (a³ + b³) = (a + b)(a² – ab + b²)

6.(a³ – b³) = (a – b)(a² + ab + b²)

7. (a³ + b³ + c³ – 3abc) = (a + b + c)(a² + b² + c² – ab – bc – ac)

8. when a + b + c = 0, then a³ + b³ + c³ = 3abc