Definition, with examples of convergent and divergent sequences.

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

The squeezing lemma and the monotone convergence test for sequences.

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

Definition, using the sequence of partial sums and the sequence of partial absolute sums. Absolutely convergent and conditionally convergent series are defined, with examples of the harmonic and alternating harmonic series.

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

Definitions of sequences and series, with examples of harmonic, geometric, and exponential series as well as a definition of convergence.

**Course Material Related to This Topic:**

Examples of the uses of manipulating or rearranging the terms of an absolutely convergent series.

18.013A

*Calculus with Applications*, Spring 2005

Prof. Daniel J. Kleitman

**Course Material Related to This Topic:**

Steps for using a spreadsheet to compute the partial sums of a series.

18.013A

*Calculus with Applications*, Spring 2005

Prof. Daniel J. Kleitman

**Course Material Related to This Topic:**

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

Determining whether a given series converges or diverges.

- Complete exam problem 17 on page 2
- Check solution to exam problem 17 on page 1

Three questions which involve finding the sum of a geometric series, writing infinite decimals as the quotient of integers, determining whether fifteen different series converge or diverge, and using Riemann sums to show a bound on the series of sums of 1/n.

- Complete exam problems 6C–1 to 6C–3 on page 41
- Check solution to exam problems 6C–1 to 6C–3 on pages 94–6

Five questions which involve finding whether a series converges or diverges, finding the sum of a series, finding a rational expression for an infinite decimal, and finding the total distance traveled by a ball as it bounces up and down repeatedly.

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

- Complete exam problems 7A–1 to 7A–5 on page 43
- Check solution to exam problems 7A–1 to 7A–5 on page 97