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Quantitative Aptitude :: Problems on Numbers

Problems on Numbers Important Formulas


Formulas of Number Series:


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

Sum of first n odd numbers = n2

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

Some Basic Formulae:


(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)

(a3 + b3) = (a + b)(a2 - ab + b2)

(a3 - b3) = (a - b)(a2 + ab + b2)

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

When a + b + c = 0, then a3 + b3 + c3 = 3abc

(a + b)n = an + (nC1)an-1b + (nC2)an-2b2 + … + (nCn-1)abn-1 + bn