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$n$. 1 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\$.