MathDB
Putnam 1950 A4

Source:

May 24, 2022
Putnam

Problem Statement

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.
(ii) Show that x1+x31⋅3+x51⋅3⋅5+x71⋅3⋅5⋅7+⋯1+x22+x42⋅4+x62⋅4⋅6+⋯=∫0xe−t2dt. \frac{\frac x1 + \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} \mathrm dt.
Back to ProblemsView on AoPS