MathDB

Sequences

(a_n)_{n=0}^{\infty}

and

(b_n)_{n=0}^{\infty}

are defined with recurrent relations :

a_0=0 , \;\;\; a_1=1, \;\;\;\; a_{n+1}=\frac{2018}{n} a_n+ a_{n-1}\;\;\; \text {for }\;\;\; n\geq 1

and

b_0=0 , \;\;\; b_1=1, \;\;\;\; b_{n+1}=\frac{2020}{n} b_n+ b_{n-1}\;\;\; \text {for }\;\;\; n\geq 1

Prove that :

\frac{a_{1010}}{1010}=\frac{b_{1009}}{1009}

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