@SimplyBeautifulArt: Hmm. This seems borderline. It was originally a Please-Solve-Question and hence the duplicates identified answered the question, but after the asker edited to include his/her attempt, it is now different since the question is now about whether the attempt is correct. Jack has added the
proof-verification tag, and I agree and will also vote to reopen. By the way, J. Jenkins, your attempt is
wrong because if you can't split a limit into a sum of $n$ terms where $n$ is
undefined. —
user21820 4 mins ago