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Friday, 11 August 2017

Maths Expression Basic


Algebra identities

     a2 - b2 = (a-b)(a+b)

  • a3 - b3 = (a - b)(a2+ ab + b2)
  • a3 + b3 = (a + b)(a2 - ab + b2)
  • (a + b)2 = a2 + 2ab + b2
  • (a - b)2 = a2 - 2ab +b2
  • (a + b)3 = a3 + 3a2b + 3ab2 + b3
  • (a - b)3 = a3 - 3a2b + 3ab2 - b3
  • ----------------------------------------------------------------------------------------------------------------------------
Consider the following arithmetic progression:
  • a + (a + d) + (a + 2d) + (a + 3d) + ...
  • a is the initial term
  • d is the common difference
Nth Term, Tn = a + (n - 1)d
    • The sum of the first n terms of the arithmetic progression is:
      • Sum of the first n term, Sn = n/2[2a + (n-1)d]
      • -----------------------------------------------------------------------------------------
      • Consider the following geometric progression:
        • a + ar + ar2 + ar3 + ...
        • a is the scale factor
        • r is the common ratio
        • Nth Term , Tn = ar n - 1
        • The sum of the first n terms, Sn is:
          • sum of the first n term, Sn = [a(1-r^n)]/[1-r]
        • ------------------------------------------------------------------------------------------------------------------------



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