# Reelle Zahlen/Rationale Folgen/Konvergenzverhalten/Aufgabe/en

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Let ${\displaystyle {}P=\sum _{i=0}^{d}a_{i}x^{i}}$ and ${\displaystyle {}Q=\sum _{i=0}^{e}b_{i}x^{i}}$ be polynomials with ${\displaystyle {}a_{d},b_{e}\neq 0}$. Determine, depending on ${\displaystyle {}d}$ and ${\displaystyle {}e}$, whether

${\displaystyle z_{n}={\frac {P(n)}{Q(n)}}}$

(which is defined for ${\displaystyle {}n}$ sufficiently large) is a convergent sequence or not, and determine the limit in the convergent case.