Examples of General Elementary Series

Here follows a collection of examples of general, elementary series. The reader is also referred to Calculus 3b. The main subject is Power series; but first we must consider series in general. We shall in Calculus 3c-3 return to the power series.

Finally, even if I have tried to write as careful as possible, I doubt that all errors have been removed. I hope that the reader will forgive me the unavoidable errors.

Leif Mejlbro

• Introduction

1. Partial sums and telescopic series
2. Simple convergence criteria for series
3. The integral criterion
4. Small theoretical examples
5. Conditional convergence and Leibniz’s criterion
6. Series of functions; uniform convergence