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Omni-MATH / Let a₁,a₂,… be a sequence defined by a₁=a₂=1 and a_(n+2)=a_(n+1)+a_(n) for n≥1. Find ∑_(n=1)^(∞)(a_(n))/(4^(n+1))

Problem

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problem

Let a1,a2,…a_{1}, a_{2}, \ldots be a sequence defined by a1=a2=1a_{1}=a_{2}=1 and an+2=an+1+ana_{n+2}=a_{n+1}+a_{n} for n≥1n \geq 1. Find ∑n=1∞an4n+1\sum_{n=1}^{\infty} \frac{a_{n}}{4^{n+1}}
Plain-text mathematical notation (without MathML)
Let a₁,a₂,… be a sequence defined by a₁=a₂=1 and a_(n+2)=a_(n+1)+a_(n) for n≥1. Find ∑_(n=1)^(∞)(a_(n))/(4^(n+1))
Original LaTeX notation
Let $a_{1}, a_{2}, \ldots$ be a sequence defined by $a_{1}=a_{2}=1$ and $a_{n+2}=a_{n+1}+a_{n}$ for $n \geq 1$. Find $$\sum_{n=1}^{\infty} \frac{a_{n}}{4^{n+1}}$$

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Source and history

task_id
1846a9e7-2080-57e2-8a96-8139e8033b60
task_key
test--1846a9e7-2080-57e2-8a96-8139e8033b60
task_revision_id
1
config / split
/ test

Official source

initial import