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Omni-MATH / A sequence of real numbers x₁,x₂,…,x_(n) is given such that x_(i+1)=x_(i)+(1)/(30000)√(1−x_(i)²), i=1,2,…, and x₁=0. Can n be equal to 50000 if x_(n)<1?

Problem

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problem

A sequence of real numbers x1,x2,…,xnx_1,x_2,\ldots ,x_n is given such that xi+1=xi+1300001−xi2,i=1,2,…,x_{i+1}=x_i+\frac{1}{30000}\sqrt{1-x_i^2},\ i=1,2,\ldots , and x1=0x_1=0. Can nn be equal to 5000050000 if xn<1x_n<1?
Plain-text mathematical notation (without MathML)
A sequence of real numbers x₁,x₂,…,x_(n) is given such that x_(i+1)=x_(i)+(1)/(30000)√(1−x_(i)²), i=1,2,…, and x₁=0. Can n be equal to 50000 if x_(n)<1?
Original LaTeX notation
A sequence of real numbers $x_1,x_2,\ldots ,x_n$ is given such that $x_{i+1}=x_i+\frac{1}{30000}\sqrt{1-x_i^2},\ i=1,2,\ldots ,$ and $x_1=0$. Can $n$ be equal to $50000$ if $x_n<1$?

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Source and history

task_id
5af3b4f4-ac3c-5650-818d-6e6c56f9b8cc
task_key
test--5af3b4f4-ac3c-5650-818d-6e6c56f9b8cc
task_revision_id
1
config / split
/ test

Official source

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