Tuesday, 23 July 2019

radicals - Prove or disprove that sqrt2+frac1n is irrational for ninmathbbZ+

I have good reason to suspect that 2+1n is irrational for all nZ+ but a proof of this eludes me. I've tried proof by contradiction have had no success. I've also tried induction where clearly the base case is true, i.e. 2+1=3 is irrational, but I haven't been able to show the induction step.

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