Infinite Series

No not Eastenders (as a tutor joked to me), but the topic of the OU's M208 book AA3. I have got through this in a fairly short space of time and I have already started the last book in this first block on analysis, continuity.

I really enjoyed AA3. I like numbers and I like sequences and series, some of which are a bit quirky at times. The good thing about this third book of analysis is that by the end of it I felt like everything was falling into place. The main emphasis is on being able to ascertain whether a series such as 1+1/2+1/3+1/4+... is convergent or not and by the end of the book all these techniques are at your fingertips. You find yourself using all the methods of AA2 on sequences as well as what is in this book, so you do feel like you are getting somewhere. I even felt that I could prove the convergence of the series for e^x for x<0.

The only slight gripe I would have is that I would have liked to have seen some more work on actually determining the sum of a convergent series as I think this can be quite interesting. For example, we are told as an aside that the sum of the series 1+1/4+1/9+1/16... is π²/6, but it would be nice to know how this is obtained.