Library / /196 of 387

, 2004

Algebra Difficulty 2.0 Junior Find the answer Canada

$\frac{1}{2}+\frac{2^1}{2^2}+\frac{2^2}{2^3}+\cdots+\frac{2^{2002}}{2^{2003}}+\frac{2^{2003}}{2^{2004}}$ is equal to

(A) $1002$ (B) $501$ (C) $\frac{1}{2^{2004}}$ (D) $2004$ (E) $\frac{2004}{2^{2004}}$

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.