proof that the pattern exists for all n – math.stackexchange.com

proof that the pattern exists for all n – math.stackexchange.com

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Explain the pattern $$(\sqrt2-1)^1= \sqrt2 - \sqrt1$$ $$(\sqrt2-1)^2 = \sqrt9 - \sqrt8$$ $$ (\sqrt2-1)^3 = \sqrt{50} - \sqrt{49} $$ that is $(\sqrt2-1)^n$ is equal to difference of ...

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