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Showing posts from December 16, 2011

quicker maths

ALGEBRA : 1.      Sum of first n natural numbers = n(n+1)/22.      Sum of the squares of first n natural numbers = n(n+1)(2n+1)/63.      Sum of the cubes of first n natural numbers = [n(n+1)/2]^24.      Sum of first n natural odd numbers = n^25.      Average = (Sum of items)/Number of items
Arithmetic Progression (A.P.): An A.P. is of the form a, a+d, a+2d, a+3d, ... where a is called the 'first term' and d is called the 'common difference' 1.      nth term of an A.P. tn =a + (n-1)d2.      Sum of the first n terms of an A.P. Sn = n/2[2a+(n-1)d] or Sn = n/2(first term + last term)
Geometrical Progression (G.P.): A G.P. is of the form a, ar, ar2, ar3, ... where a is called the 'first term' and r is called the 'common ratio'. 1.      nth term of a G.P. tn = arn-12.      Sum of the first n terms in a G.P. Sn = a|1-rn|/|1-r|
Permutations and Combinations : nPr = n!/(n-r)!nPn = n!nP1 = n
nCr = n!/(r! (n-r)!)nC1 = nnC0 = 1 = nCnnCr = nCn-rnCr = nPr/r!
Number of diagon…