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- Feb 14, 2012

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Evaluate \(\displaystyle \left\lfloor{\frac{1}{3}}\right\rfloor+\left\lfloor{\frac{2}{3}}\right\rfloor+\left\lfloor{\frac{2^2}{3}}\right\rfloor+\left\lfloor{\frac{2^3}{3}}\right\rfloor+\cdots+\left\lfloor{\frac{2^{1000}}{3}}\right\rfloor\), without the help of a calculator.

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