Let $f(x)=\prod_{n=1}^{\infty} \left( 1 + \frac{x}{2^n} \right)$. Show that at the point $x=1$, $f(x)$ and all its derivatives are irrational.
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Tags: calculus, derivative, Irrational numbers
Let $f(x)=\prod_{n=1}^{\infty} \left( 1 + \frac{x}{2^n} \right)$. Show that at the point $x=1$, $f(x)$ and all its derivatives are irrational.