Gamma!

\[ \large \gamma = \int_0^1 \left( \dfrac n{1-x^n} - \dfrac1{1-x} \right) \sum_{k=1}^\infty x^{n^k - 1} \, dx \]

Prove that the equation holds true for constant $n$ .

Notation: $\gamma$ denote the Euler-Mascheroni constant.

This is a part of the set Formidable Series and Integrals

#Calculus

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$