MathDB
2021 Individual #15

Source:

April 28, 2022
2021 Individual

Problem Statement

Which of the following answer choices is the closest approximation to 34+78+1516+⋯+10231024=22−122+23−123+⋯+210−1210?\dfrac34+\dfrac78+\dfrac{15}{16}+\cdots+\dfrac{1023}{1024} = \dfrac{2^2-1}{2^2}+\dfrac{2^3-1}{2^3}+\cdots+\dfrac{2^{10}-1}{2^{10}}?
<spanclass=′latex−bold′>(A)</span>152<spanclass=′latex−bold′>(B)</span>8<spanclass=′latex−bold′>(C)</span>172<spanclass=′latex−bold′>(D)</span>9<spanclass=′latex−bold′>(E)</span>192<span class='latex-bold'>(A) </span>\dfrac{15}{2}\qquad<span class='latex-bold'>(B) </span>8\qquad<span class='latex-bold'>(C) </span>\dfrac{17}{2}\qquad<span class='latex-bold'>(D) </span>9\qquad<span class='latex-bold'>(E) </span>\dfrac{19}{2}
Back to ProblemsView on AoPS