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Problem 333

Algebra Difficulty 2.0 Find the answer CEMC Cayley · Canada · 2004

$\frac{1}{2}+\frac{2^1}{2^2}+\frac{2^2}{2^3}+\cdots+\frac{2^{2002}}{2^{2003}}+\frac{2^{2003}}{2^{2004}}$ is equal to (A) $1002$ (B) $501$ (C) $\frac{1}{2^{2004}}$ (D) $2004$ (E) $\frac{2004}{2^{2004}}$

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