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MATH / Let x and y be real numbers such that −1<x<y<1. Let G be the sum of the infinite geometric series whose first term is x and whose common ratio is y, and let G' be the sum of the in…

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problem

Let xx and yy be real numbers such that −1<x<y<1.-1 < x < y < 1. Let GG be the sum of the infinite geometric series whose first term is xx and whose common ratio is y,y, and let $G'$ be the sum of the infinite geometric series whose first term is yy and whose common ratio is x.x. If $G = G',$ find x+y.x + y.
Plain-text mathematical notation (without MathML)
Let x and y be real numbers such that −1<x<y<1.  Let G be the sum of the infinite geometric series whose first term is x and whose common ratio is y, and let $G'$ be the sum of the infinite geometric series whose first term is y and whose common ratio is x.  If $G = G',$ find x+y.
Original LaTeX notation
Let $x$ and $y$ be real numbers such that $-1 < x < y < 1.$  Let $G$ be the sum of the infinite geometric series whose first term is $x$ and whose common ratio is $y,$ and let $G'$ be the sum of the infinite geometric series whose first term is $y$ and whose common ratio is $x.$  If $G = G',$ find $x + y.$

level

Level 3

type

Intermediate Algebra

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Source and history

task_id
4d8a42ef-5652-5b39-b94c-29c5362b9ad9
task_key
intermediate~5falgebra--test--4d8a42ef-5652-5b39-b94c-29c5362b9ad9
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import