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MATH / An infinite geometric series has sum 2000. A new series, obtained by squaring…

Problem

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problem

An infinite geometric series has sum 2000. A new series, obtained by squaring each term of the original series, has sum 16 times the sum of the original series. The common ratio of the original series is

m/n

, where

m

and

n

are relatively prime positive integers. Find

m+n

Plain-text mathematical notation (without MathML)

An infinite geometric series has sum 2000.  A new series, obtained by squaring each term of the original series, has sum 16 times the sum of the original series.  The common ratio of the original series is m/n, where m and n are relatively prime positive integers. Find m+n.

Original LaTeX notation

An infinite geometric series has sum 2000.  A new series, obtained by squaring each term of the original series, has sum 16 times the sum of the original series.  The common ratio of the original series is $m/n$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

level

Level 5

type

Algebra

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task_id: 68b434f6-1493-5ce7-98ea-c909ae1a4f74
task_key: algebra--test--68b434f6-1493-5ce7-98ea-c909ae1a4f74
task_revision_id: 2
config / split: algebra / test

Official source

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