May 28th, 2015
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A variable is a symbol that represents a number. Usually we use letters such as n, t, or x for variables. For example, we might say that s stands for the side-length of a square

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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 = n25.Average = (Sum of items)/Number of itemsArithmetic 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 :1.nPr = n!/(n-r)!2.nPn = n!3.nP1 = n1.nCr = n!/(r! (n-r)!)2.nC1 = n3.nC0 = 1 = nCn4.nCr = nCn-r5.nCr = nPr/r!Number of diagonals in a geometric figure of n sides = nC2-nTests of Divisibility :1.A number is divisible by 2 if it is an even number.2.A number is divisible by 3 if the sum of the digits is divisible by 3.3.A number is divisible by 4 if the number formed by the last two digits is divisible by 4.4.A number is divisible by 5 if the units digit is either 5 or 0.5.A number is divisible by 6 if the number is divisible by both 2 and 3.6.A number is divisible by 8 if the number formed by the last three digits is divisible by 8.7.A number is divisibl

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