Context free grammar for the language {a^{i}b^{j}, j> 2i}

Question

I tried to do it by myself and got this answer but this way of deducing the answer doesn't seem to match anyone's answer on the internet.

$$S \rightarrow aSbbB$$

$$B \rightarrow bB|\epsilon$$

Am I missing something?

Answer 1

Yes, you're missing something. Actually two things. First, if every instance of $B$ is chosen as $\epsilon$, you're left with a case where $j=2i$ rather than $j>2i$. Second, Every $S$ in your grammar contains another $S$ so it only produces infinite strings.