olymmath

HMMT 2003 U4

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Let z=1−2iz=1-2 i. Find 1z+2z2+3z3+⋯\frac{1}{z}+\frac{2}{z^{2}}+\frac{3}{z^{3}}+\cdots.

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{2i-1}{4}

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