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Rational limit

Let \mathbb{N} \ni n \geq 2. Evaluate the limit

    \[\ell = \lim_{x \rightarrow 1} \frac{\left ( 1-\sqrt{x} \right )\left ( 1-\sqrt[3]{x} \right )\left ( 1-\sqrt[4]{x} \right ) \cdots \left ( 1-\sqrt[n]{x} \right )}{\left ( 1-x \right )^{n-1}}\]

Solution

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