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English

A book with a collection of examples of general, elementary series.

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*Leif Mejlbro* was educated as a mathematician at the *University of Copenhagen*, where he wrote his thesis on *Linear Partial Differential Operators and Distributions*. Shortly after he obtained a position at the *Technical University of Denmark*, where he remained until h...

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A book with a collection of 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**