CFG for $\{a^i b^j : 2 i<j\}$
You can derive $aabbb$ which is not in the language, so your grammar is wrong.

How did I find this? I observed that $A \Rightarrow^* a^ib^i$ and $B \Rightarrow^* b^j$ for all $i \geq 0$, $j &gt; 0$. It's clear that this is wrong, and I looked for the smallest counter-example.

You need to ensure that more than double as many $b$'s as $a$'s are generated.