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Omni-MATH / An infinite sequence of real numbers a₁,a₂,… satisfies the recurrence a_(n+3)=a_(n+2)−2a_(n+1)+a_(n) for every positive integer n. Given that a₁=a₃=1 and a₉₈=a₉₉, compute …

Problem

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problem

An infinite sequence of real numbers a1,a2,…a_{1}, a_{2}, \ldots satisfies the recurrence an+3=an+2−2an+1+ana_{n+3}=a_{n+2}-2 a_{n+1}+a_{n} for every positive integer nn. Given that a1=a3=1a_{1}=a_{3}=1 and a98=a99a_{98}=a_{99}, compute a1+a2+⋯+a100a_{1}+a_{2}+\cdots+a_{100}.
Plain-text mathematical notation (without MathML)
An infinite sequence of real numbers a₁,a₂,… satisfies the recurrence a_(n+3)=a_(n+2)−2a_(n+1)+a_(n) for every positive integer n. Given that a₁=a₃=1 and a₉₈=a₉₉, compute a₁+a₂+⋯+a₁₀₀.
Original LaTeX notation
An infinite sequence of real numbers $a_{1}, a_{2}, \ldots$ satisfies the recurrence $$a_{n+3}=a_{n+2}-2 a_{n+1}+a_{n}$$ for every positive integer $n$. Given that $a_{1}=a_{3}=1$ and $a_{98}=a_{99}$, compute $a_{1}+a_{2}+\cdots+a_{100}$.

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Source and history

task_id
e33d04fe-198e-5842-9816-919cf38eb536
task_key
test--e33d04fe-198e-5842-9816-919cf38eb536
task_revision_id
1
config / split
/ test

Official source

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