Prove $\forall a>0.BPP[{a,a+\frac{1}{n}}]=BPP$

Question

I need to prove that

$\forall a>0.BPP[{a,a+\frac{1}{n}}]=BPP$

$BPP[a,b]$ definition:

A language L is in BPP(a,b) if and only if there exists a probabilistic Turing machine M, such that

M runs for polynomial time on all inputs For all x in L, M outputs 1 with probability greater than or equal to b For all x not in L, M outputs 1 with probability less than or equal to a

I've tried using the Amplifying Lemmas and then Chernoff Inequality, when my sketch of proof was to run the probabilistic Turing Machine on the input $k$, times and then accept or reject according to majority of accepting or rejecting of the simulated runs.

My problem is with the choosing of $k$. No value that I chose could work with the lower and upper bounds.

Am I in the right direction? Could I get a tip regarding $k$?