I have the following inquality
where c>0 is a fixed constant and (a_n)_n is a positive real sequence.
I think I can't solve it explicetly.
But I would like to prove that if there exist K>0 and k>0 such that
a_n >= K e^(k n) for any n positive integer
then the inequality is verified for any n big enough.
Do you think it's true? Do you know how to prove it?