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====== Math 445 lecture 10: more ''for'' ====== Here's a in finite series for $pi^2/6$ \begin{eqnarray*} & & \frac{3}{4 \pi} \sqrt{4 \cdot x^2 12}\\ & & \lim_{n \to \infty} \sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6}\\ & & {\it f}(x) = \frac{1}{\sqrt{x} x^2}\\ & & e^{i \pi} + 1 = 0\; \end{eqnarray*} \begin{eqnarray*} \pi^2/6 = 1 + 1/2^2 + 1/3^2 + 1/4^2 + 1/5^2 + \ldots \end{eqnarry*}