Getting rid of nasty cutoffs

Smoothing sums

Use analytic expressions of constraints in sums or integrals

Partial summation When is this useful? ( If you have a sum of the form , partial summation allows you to replace the sequences and by the difference sequence and the partial-sums sequence . Partial summation is useful if the sum is easier to handle than the sum . (It is the discrete analogue of integration by parts.))

Bounding the sum by an integral

Contributions wanted This article could use additional contributions. Many more articles wanted here, starting with very basic ones on topics that would appear in a first course on analysis.