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Fancy integral

Author: anonymous
Problem has been solved: 30 times

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Let $f(x) = x^{10} + x^{9} + \ldots + 1$ and $\frac{a}{b} = \lim_{n \to \infty} \int_0^1 \ldots \int_0^1 f\left(\frac{x_1 + \ldots + x_n}{n}\right) dx_1 \ldots dx_n$ where $a, b$ are coprime positive integers. Find $a + b$.






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