Show a set of numbers are irrational

Moderator: elim

Show a set of numbers are irrational

Postby elim » Sat Feb 04, 2012 10:18 am

Suppose that $p,q\in\mathbb{N}^+$ and $\exp(1)\cdot (\sqrt{p+q}-\sqrt{q})^2 < 1$,

Show that $\displaystyle{\ln\left(1+\frac{p}{q} \right ) } $ is irrational.

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