Abel Summation by Parts

Abel's summation by parts formula is a discrete analogue of integration by parts. It relates the sum of products of two sequences to the product of their partial sums and differences.

Experiment

In the Abel Summation by Parts module, you can explore the relationship between the weighted sum, boundary term, and correction sum for different sequences and weights.

To see this in action:

1. Set the Sequence control to Alternating.
2. Set the Weights control to Reciprocal.
3. Observe the Partial sums plot and note that they alternate between 1 and 0, ensuring they are bounded.
4. Increase the Terms control and observe the Boundary term output approach 0, illustrating Dirichlet's test for convergence.