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Omni-MATH / Let z₀+z₁+z₂+⋯ be an infinite complex geometric series such that z₀=1 and z₂₀₁₃=(1)/(2013²⁰¹³). Find the sum of all possible sums of this series.

Problem

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problem

Let z0+z1+z2+⋯z_{0}+z_{1}+z_{2}+\cdots be an infinite complex geometric series such that z0=1z_{0}=1 and z2013=120132013z_{2013}=\frac{1}{2013^{2013}}. Find the sum of all possible sums of this series.
Plain-text mathematical notation (without MathML)
Let z₀+z₁+z₂+⋯ be an infinite complex geometric series such that z₀=1 and z₂₀₁₃=(1)/(2013²⁰¹³). Find the sum of all possible sums of this series.
Original LaTeX notation
Let $z_{0}+z_{1}+z_{2}+\cdots$ be an infinite complex geometric series such that $z_{0}=1$ and $z_{2013}=\frac{1}{2013^{2013}}$. Find the sum of all possible sums of this series.

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Source and history

task_id
80e4604b-830c-51ba-9ded-a1a8a7b2c28f
task_key
test--80e4604b-830c-51ba-9ded-a1a8a7b2c28f
task_revision_id
1
config / split
/ test

Official source

initial import