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Omni-MATH / Let u and v be real numbers such that (u+u²+u³+⋯+u⁸)+10u⁹=(v+v²+v³+⋯+v¹⁰)+10v¹¹=8. Determine, with proof, which of the two numbers, u or v , is larger.

Problem

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problem

Let

u

and

v

be real numbers such that

(u + u^2 + u^3 + \cdots + u^8) + 10u^9 = (v + v^2 + v^3 + \cdots + v^{10}) + 10v^{11} = 8.

Determine, with proof, which of the two numbers,

u

v

, is larger.

Plain-text mathematical notation (without MathML)

Let u and v be real numbers such that (u+u²+u³+⋯+u⁸)+10u⁹=(v+v²+v³+⋯+v¹⁰)+10v¹¹=8. Determine, with proof, which of the two numbers, u or v , is larger.

Original LaTeX notation

Let $u$ and $v$ be real numbers such that \[(u + u^2 + u^3 + \cdots + u^8) + 10u^9 = (v + v^2 + v^3 + \cdots + v^{10}) + 10v^{11} = 8.\] Determine, with proof, which of the two numbers, $u$ or $v$ , is larger.

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Source and history

task_id: c40b29fd-0735-566d-b4b9-8dd4eb434238
task_key: test--c40b29fd-0735-566d-b4b9-8dd4eb434238
task_revision_id: 4
config / split: / test

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