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minus_twelve_._note [2019/09/09 22:33]
nikolaj
minus_twelve_._note [2019/09/09 22:45] (current)
nikolaj
Line 56: Line 56:
  
 So as an example, with $k=3,​a=2,​b=4$ you get the identity So as an example, with $k=3,​a=2,​b=4$ you get the identity
-$$\frac{1}{3}(4^3-2^3)=(2^2+3^2)+\frac{1}{2}(4^2-2^2)-\frac{1}{12}\,​2\,​(4^1-2^1)$$+$$\frac{1}{3}(4^3-2^3)=(2^2+(4-1)^2)+\frac{1}{2}(4^2-2^2)-\frac{1}{12}\,​2\,​(4^1-2^1)$$
 and there are literally infinitely many identities involving $-\frac{1}{12}$ because of this formula. In case you're wondering, both sides of the equation above simplify to $\tfrac{56}{3}$. and there are literally infinitely many identities involving $-\frac{1}{12}$ because of this formula. In case you're wondering, both sides of the equation above simplify to $\tfrac{56}{3}$.
  
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