Since you asked...
I took a look at your post, and it is at best unclear. Labelled as a "hint", you suggest "add an infinite amount of the limit" to prove the proposition.
And that's all you wrote.
There are a number of community members who will post hints as answers, but when challenged the typical response is to add more detail to the post until a complete answer emerges.
You've responded by complaining about unfairness. If you can give a coherent proof, it would serve future readers to fill in what can easily be argued is a gap in your present answer.
I'll provide more specifics as Comments to your Answer, but if you have improvements to make to the Answer, it would be timely to do so in view of the downvotes.