English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The aim of this note is to sum the series of type, where, the sequencerepeats  k -periodically and the sum of its first  k  terms vanishes. Using elementary methods, we can transform this series to a definite integral, suitable for students of Calculus to work with. We include several examples and discuss how to write the integrals involved in terms of the digamma function. If  λ  is a rational, the sum can be evaluated explicitly. We give a proof of the explicit value of Dirichlet  L -series as an application at  s  = 1.

Sum of alternating-like series as definite integrals