Maple worksheets on series

More calculus topics:

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

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