MathDB

2016 Algebra #5

Source:

December 24, 2016

Problem Statement

An infinite sequence of real numbers

a_1, a_2, \dots

satisfies the recurrence

a_{n+3} = a_{n+2} - 2a_{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 + \dots + a_{100}