2021 JMPSC Invitationals Problems/Problem 4
Problem
Let and
be sequences of real numbers such that
,
, and, for all positive integers
,
Find
.
Solution
We notice that Given that
and
in the problem, we can plug this in to get that
We can use the same method to conclude that
Adding this system of equations and
gives us
Dividing both sides by
, results in
~mahaler