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Omni-MATH / A sequence {a_(n)}_(n≥1) of positive reals is defined by the rule a_(n+1)a_(n−1)⁵=a_(n)⁴a_(n−2)² for integers n>2 together with the initial values a₁=8 and a₂=64 and a₃=1024. Compu…

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problem

A sequence {an}n≥1\left\{a_{n}\right\}_{n \geq 1} of positive reals is defined by the rule an+1an−15=an4an−22a_{n+1} a_{n-1}^{5}=a_{n}^{4} a_{n-2}^{2} for integers n>2n>2 together with the initial values a1=8a_{1}=8 and a2=64a_{2}=64 and a3=1024a_{3}=1024. Compute a1+a2+a3+⋯\sqrt{a_{1}+\sqrt{a_{2}+\sqrt{a_{3}+\cdots}}}
Plain-text mathematical notation (without MathML)
A sequence {a_(n)}_(n≥1) of positive reals is defined by the rule a_(n+1)a_(n−1)⁵=a_(n)⁴a_(n−2)² for integers n>2 together with the initial values a₁=8 and a₂=64 and a₃=1024. Compute √(a₁+√(a₂+√(a₃+⋯)))
Original LaTeX notation
A sequence $\left\{a_{n}\right\}_{n \geq 1}$ of positive reals is defined by the rule $a_{n+1} a_{n-1}^{5}=a_{n}^{4} a_{n-2}^{2}$ for integers $n>2$ together with the initial values $a_{1}=8$ and $a_{2}=64$ and $a_{3}=1024$. Compute $$\sqrt{a_{1}+\sqrt{a_{2}+\sqrt{a_{3}+\cdots}}}$$

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Source and history

task_id
8944a0ce-645f-58eb-a5f6-468efb932296
task_key
test--8944a0ce-645f-58eb-a5f6-468efb932296
task_revision_id
1
config / split
/ test

Official source

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