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Omni-MATH / Let g₁(x)=(1)/(3)(1+x+x²+⋯) for all values of x for which the right hand side converges. Let g_(n)(x)=g₁(g_(n−1)(x)) for all integers n≥2. What is the largest integer r such that …

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problem

Let g1(x)=13(1+x+x2+⋯)g_{1}(x)=\frac{1}{3}\left(1+x+x^{2}+\cdots\right) for all values of xx for which the right hand side converges. Let gn(x)=g1(gn−1(x))g_{n}(x)=g_{1}\left(g_{n-1}(x)\right) for all integers n≥2n \geq 2. What is the largest integer rr such that gr(x)g_{r}(x) is defined for some real number xx ?
Plain-text mathematical notation (without MathML)
Let g₁(x)=(1)/(3)(1+x+x²+⋯) for all values of x for which the right hand side converges. Let g_(n)(x)=g₁(g_(n−1)(x)) for all integers n≥2. What is the largest integer r such that g_(r)(x) is defined for some real number x ?
Original LaTeX notation
Let $g_{1}(x)=\frac{1}{3}\left(1+x+x^{2}+\cdots\right)$ for all values of $x$ for which the right hand side converges. Let $g_{n}(x)=g_{1}\left(g_{n-1}(x)\right)$ for all integers $n \geq 2$. What is the largest integer $r$ such that $g_{r}(x)$ is defined for some real number $x$ ?

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Source and history

task_id
2aff1869-17c2-52fb-b2eb-e29e1602106c
task_key
test--2aff1869-17c2-52fb-b2eb-e29e1602106c
task_revision_id
1
config / split
/ test

Official source

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