Important formulas of maths for competitive exams

• n(n + 1)(2n + 1) is always divisible by 6.

• 32n leaves remainder = 1 when divided by 8

• n3 + (n + 1 )3 + (n + 2 )3 is always divisible by 9

• 102n + 1 + 1 is always divisible by 11

• n(n2– 1) is always divisible by 6

• n2+ n is always even

• 23n-1 is always divisible by 7

• 152n-1 +1 is always divisible by 16

• n3 + 2n is always divisible by 3

• 34n – 4 3n is always divisible by 17

• n! + 1 is not divisible by any number between 2 and n.(where n! = n (n – 1)(n – 2)(n – 3)…….3.2.1).

for example, 5! = 5.4.3.2.1 = 120 and similarly 10! = 10.9.8…….2.1= 3628800

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