How Can I Deepen My Understanding of Infinite Series and Sequences?

[swill777]

Hello.

Having already learned about infinite series and sequences in my calculus class, I'm quite interested in them and especially in learning more about them. If any of you have in mind any good books on the subject which you can recommend to me, it will be very much appreciated.

Thank you.

 

[micromass]

To know more about them, you have to do analysis. They are absolutely fundamental there.
Unfortunately, analysis is not very easy and is quite proof-based.

If you're interested in pursuing analysis, then you should probably start with "Calculus" by Spivak, which is a nice "introduction" to analysis. It's not a very easy book though and it requires you to be very familiar with proofs.

After a first introduction to analysis, you might want to take a look at interesting topics such as Fourier series.