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Calculus Level 4

\[ \large{ \begin{eqnarray} &1& + \frac1{1!}\cdot\frac{\alpha \beta}{\gamma} x + \frac1{2!} \cdot\frac{\alpha(\alpha+1) \beta(\beta+1)}{\gamma(\gamma+1)} x^2 \\ &&+ \frac1{3!} \cdot\frac{\alpha(\alpha+1)(\alpha+2) \beta(\beta+1)(\beta+2)}{\gamma(\gamma+1)(\gamma+2)} x^3+\ldots \end{eqnarray} } \]

What is the condition for which the above series is convergent for natural numbers \(\alpha,\beta,\gamma\)?

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