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 + …..
2. Basic Formulas:
- a2 – b2 = (a – b)(a + b)
- (a + b)2 = a2 + 2ab + b2.
- a2 + b2 = (a + b)2 – 2ab.
- (a – b)2 = a2 – 2ab + b2.
- (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca.
- (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca.
- (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
- (a + b)(a - b) = (a2 - b2) (a + b)2 = (a2 + b2 + 2ab) (a - b)2 = (a2 + b2 - 2ab) (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
3. 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)
