benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / The sequence (x_(n)) satisfies x₀=3 and

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

The sequence (xn)(x_n) satisfies x0=3x_0 = 3 and xn=1+xn−11−xn−1x_n = \frac{1 + x_{n - 1}}{1 - x_{n - 1}}for all ≥1.\ge 1. Find x12345.x_{12345}.
Plain-text mathematical notation (without MathML)
The sequence (x_(n)) satisfies x₀=3 and
x_(n)=(1+x_(n−1))/(1−x_(n−1))for all ≥1.  Find x₁₂₃₄₅.
Original LaTeX notation
The sequence $(x_n)$ satisfies $x_0 = 3$ and
\[x_n = \frac{1 + x_{n - 1}}{1 - x_{n - 1}}\]for all $\ge 1.$  Find $x_{12345}.$

level

Level 4

type

Intermediate Algebra

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
e573577e-233c-52b5-8614-f55fdd435b1c
task_key
intermediate~5falgebra--test--e573577e-233c-52b5-8614-f55fdd435b1c
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import