Maple worksheets on series |

More calculus topics:

- Infinite Series
- Hyperbolic Functions
- Multi-variable calculus
- The Lambert W function

The following Maple worksheets can be downloaded.

They are all compatible with

Classic Worksheet Maple 10.

An introduction to series- series.mws

- Examples of convergent sequences
- Divergent sequences
- Series and convergence of series
- Geometric series
- Convergence of bounded monotonic sequences

Convergence of series- converge.mws

- Examples infinite series
- The comparison test for convergence

The harmonic series- harmonic.mws

- Calculations of partial sums of the harmonic series
- Euler's constant

Slow-growing divergent series- worms.mws

- An example of a slow growing divergent series
- Clifford Pickover's "infinity worms"

Alternating series and absolute convergence- altabs.mws

- Alternating series
- Absolutely convergent series

The integral test for convergence of series- inttest.mws

- The integral test
- p- series

Ratio tests for convergence of series- ratio.mws

- The ratio test
- Raabe's test

Bracketing terms of series and connection with convergence- bracket.mws

- Bracketing terms of a series
- Bracketing and convergence

Euler's transformation of an alternating series- eulersum.mws

- Example's of applying Euler's transformation to an alternating series
- Derivation of Euler's transformation formula
- Symbolic construction of Euler's transformation formula
- Wijngaarden's modification of Euler's transformation
- A procedure which uses Euler's transformation to sum a series numerically:
eulersum

Levin's u transform- levinsum

- Levin's u transform
- A procedure for constructing Levin's u transform:
levinU- Levin's u transform of some standard series
- A procedure which uses Levin's u transform to sum a series numerically:
levinsum

The Euler-Maclaurin summation formula- eulermac.mws

- Euler's integral summation formula
- Certain Fourier series involving Bernoulli polynomials and Bernoulli numbers
- Sums of p-series where p is even
- Derivation of the Euler-Maclaurin summation formula
- The Euler-Maclaurin summation formula for infinite series

Summing series using the Euler-Maclaurin summation formula- EMsum.mws

- Examples involving an application of the Euler-Maclaurin summation formula
- A procedure which uses the Euler-Maclaurin summation formula to sum a series numerically:
EMsum

Rearrangement of series- rearrange.mws

- Rearrangement of terms in a conditionally convergent series
- A procedure for rearranging the terms of an alternating series:
arrange

Procedures for series- series.zip