Problem #PRU-109715

Problems Algebra and arithmetic Sequences Progressions Geometric progression Calculus Real numbers Integer and fractional parts. Archimedean property Sums of number sequences and difference series

Problem

Find the sum $1 / 3 + 2 / 3 + 2^{2} / 3 + 2^{3} / 3 + \dots + 2^{1000} / 3$ .

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