It is easy to see that $\sqrt{2}$ and $\sqrt{2}+\sqrt{3}$ are irrational. So $\sqrt{2}+\sqrt{3} + \sqrt{4}$ is irrational. But what about $\sqrt{2}+\sqrt{3} + \sqrt{4} + \sqrt{5}$? I suspect that
$$\sum_{n=2}^{k} \sqrt{n}$$ is always irrational, is it true and is there a simple way to proof that?
Sunday 15 January 2017
summation - Can $sum_{n=2}^{k} sqrt{n}$ be rational?
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