MathDB

9

Part of 2005 Harvard-MIT Mathematics Tournament

Problems(3)

2005 Algebra #9: 27,000,001

Source:

4/29/2013
The number 27, 000, 00127,\,000,\,001 has exactly four prime factors. Find their sum.
2005 Calculus #9: A sum!

Source:

4/29/2013
Compute ∑k=0∞4(4k)!. \displaystyle\sum_{k=0}^{\infty} \dfrac {4}{(4k)!}.
calculustrigonometry
2005 Geometry #9: Circle and Point Mumbo Jumbo

Source:

5/16/2013
Let ACAC be a diameter of a circle ω \omega of radius 11, and let DD be a point on ACAC such that CD=15CD=\frac{1}{5}. Let BB be the point on ω\omega such that DBDB is perpendicular to ACAC, and EE is the midpoint of DBDB. The line tangent to ω\omega at BB intersects line CECE at the point XX. Compute AXAX.
geometryanalytic geometrygraphing linesslope