Putnam 1950 A4

Answer either (i) or (ii). (i) In a right prism with triangular base, given the sum of the areas of three mutually adjacent faces (that is, of two lateral faces and one base), show that these faces are of equal area and perpendicular to each other when the volume attains its maximum. (page 292) (ii) Show that $\frac{\frac{x}{1}+\frac{x^{3}}{1 \cdot 3}+\frac{x^{5}}{1 \cdot 3 \cdot 5}+\frac{x^{7}}{1 \cdot 3 \cdot 5 \cdot 7}+\cdots}{1+\frac{x^{2}}{2}+\frac{x^{4}}{2 \cdot 4}+\frac{x^{6}}{2 \cdot 4 \cdot 6}+\cdots}=\int_{0}^{x} e^{-t^{2 / 2}} d t .$

Dataset text PutnamGAP. Quoted with source.

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