A good example that my Honors Calc prof gave me is the following: $\zeta(n)=\int_{[0,1]^{n}}\left(1-\prod_{k=1}^{n}x_{k}\right)^{-1}d\boldsymbol{x}$$ \zeta(n) = \int_{[0,1]^n}\frac{d\boldsymbol x}{1-x_1\dotsm x_n} $$ The proof is a surprisingly simple an easy induction argument on $n$.
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A good example that my Honors Calc prof gave me is the following: $\zeta(n)=\int_{[0,1]^{n}}\left(1-\prod_{k=1}^{n}x_{k}\right)^{-1}d\boldsymbol{x}$ The proof is a surprisingly simple induction argument on $n$. |
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