Number System Formulas

Number System Formulas

  1. 1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2
  2. (12 + 22 + 32 + ….. + n2) = n ( n + 1 ) (2n + 1) / 6
  3. (13 + 23 + 33 + ….. + n3) = (n(n + 1)/ 2)2
  4. Sum of first n odd numbers = n2
  5. Sum of first n even numbers = n (n + 1)
  6. (a + b)(a – b) = (a2 – b2)
  7. (a + b)2 = (a2 + b2 + 2ab)
  8. (a – b)2 = (a2 + b2 – 2ab)
  9. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
  10. (a3 + b3) = (a + b)(a2 – ab + b2)
  11. (a3 – b3) = (a – b)(a2 + ab + b2)
  12. (a3 + b3 + c3 – 3abc) = (a + b + c)(a2 + b2 + c2 – ab – bc – ac)
  13. When a + b + c = 0, then a3 + b3 + c3 = 3abc
  14. (a + b)n = an + (nC1)an-1b + (nC2)an-2b2 + … + (nCn-1)abn-1 + bn

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