MathDB
Recurrence Sequence

Source: 1992 National High School Mathematics League, Exam One, Problem 11

February 27, 2020

Problem Statement

For real numbers a1,a2,⋯ ,a100a_1,a_2,\cdots,a_{100}, a1=a2=1,a3=2a_1=a_2=1,a_3=2. For any positive integer nn, anan+1an+2≠1,anan+1an+2an+3=an+an+1+an+2+an+3a_na_{n+1}a_{n+2}\neq1,a_na_{n+1}a_{n+2}a_{n+3}=a_n+a_{n+1}+a_{n+2}+a_{n+3}, then a1+a2+⋯+a100=a_1+a_2+\cdots+a_{100}=________.
Back to ProblemsView on AoPS