# Reelle Exponentialreihe/Durch x^n/Unbeschränkt/Aufgabe/en

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Prove that the real exponential function defined by the exponential series has the property that for each ${\displaystyle {}d\in \mathbb {N} }$ the sequence

${\displaystyle \left({\frac {\exp n}{n^{d}}}\right)_{n\in \mathbb {N} }}$

diverges to ${\displaystyle {}+\infty }$.