I am back again with my second note! This time, I would like to share a divergent series which I find pretty interesting. Oh, just in case you are wondering, I consider my idea original.
Let's not beat around the bush, shall we?
The series is as follows:. I am going to show that the series diverges as .
For starters, I will rewrite our series as
With some observation,
we can see that and
Combining both, we have
is the harmonic series, it diverges. You can see the proof here. So, it follows that diverges.
We conclude that diverges. The proof is complete.
That's all for now. Stay tuned for more.
Do correct me if I am wrong. Also, please feel free to share your thoughts at the comment section below.