Task 249
Task 249: test task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. 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…
The task
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 $x + y.$