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2018 AMC 10BProblem 20P16-20~5 minPrint
Sequences & SeriesFunctionsCompute small cases, spot the pattern, generalizeCollapse a sum or product by cancellation

A function ff is defined recursively by f(1)=f(2)=1f(1)=f(2)=1 and f(n)=f(n−1)−f(n−2)+nf(n)=f(n-1)-f(n-2)+n for all integers n≥3n \geq 3 . What is f(2018)f(2018) ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.