Alternierende Summe/Induktion/Aufgabe

Zeige mittels vollständiger Induktion für ${}n\geq 1$ die Formel

{}\sum _{k=1}^{n}(-1)^{k}k={\begin{cases}{\frac {n}{2}}{\text{ bei }}n{\text{ gerade}},\\-{\frac {n+1}{2}}{\text{ bei }}n{\text{ ungerade}}\,.\end{cases}}\,

This article is issued from Wikiversity. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.