For a real number x, let d(x)=minn:integer (x-n)2. Evaluate the following double infinite series:
. . . + 8 d(x/8)+4 d(x/4) + 2 d(x/2) + d(x) + d(2x) / 2 + d(4x)/4 + d(8x)/8 + . . .
The best solution was submitted by Gee Won Suh (서기원), 수리과학과 2009학번. Congratulations!
Here is his Solution of Problem 2011-20.
Alternative solutions were submitted by 박승균 (수리과학과 2008학번, Alternative Solution, +3) and 장경석 (2011학번, +3).