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Omni-MATH / Define a sequence of polynomials as follows: let a₁=3x²−x, let a₂=3x²−7x+3, and for n≥1, let a_(n+2)=(5)/(2)a_(n+1)−a_(n). As n tends to infinity, what is the limit of the sum of t…

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problem

Define a sequence of polynomials as follows: let a1=3x2−xa_{1}=3 x^{2}-x, let a2=3x2−7x+3a_{2}=3 x^{2}-7 x+3, and for n≥1n \geq 1, let an+2=52an+1−ana_{n+2}=\frac{5}{2} a_{n+1}-a_{n}. As nn tends to infinity, what is the limit of the sum of the roots of ana_{n} ?
Plain-text mathematical notation (without MathML)
Define a sequence of polynomials as follows: let a₁=3x²−x, let a₂=3x²−7x+3, and for n≥1, let a_(n+2)=(5)/(2)a_(n+1)−a_(n). As n tends to infinity, what is the limit of the sum of the roots of a_(n) ?
Original LaTeX notation
Define a sequence of polynomials as follows: let $a_{1}=3 x^{2}-x$, let $a_{2}=3 x^{2}-7 x+3$, and for $n \geq 1$, let $a_{n+2}=\frac{5}{2} a_{n+1}-a_{n}$. As $n$ tends to infinity, what is the limit of the sum of the roots of $a_{n}$ ?

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task_id
bd8b92de-a0b2-5f9a-b4d4-6d824cc7562a
task_key
test--bd8b92de-a0b2-5f9a-b4d4-6d824cc7562a
task_revision_id
1
config / split
/ test

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