We value your privacy

We use cookies to enhance your browsing experience, serve personalized ads or content, and analyze our traffic. By clicking "Accept All", you consent to our use of cookies.

Customize Consent Preferences

We use cookies to help you navigate efficiently and perform certain functions. You will find detailed information about all cookies under each consent category below.

The cookies that are categorized as "Necessary" are stored on your browser as they are essential for enabling the basic functionalities of the site. ... 

Always Active

Necessary cookies are required to enable the basic features of this site, such as providing secure log-in or adjusting your consent preferences. These cookies do not store any personally identifiable data.

No cookies to display.

Functional cookies help perform certain functionalities like sharing the content of the website on social media platforms, collecting feedback, and other third-party features.

No cookies to display.

Analytical cookies are used to understand how visitors interact with the website. These cookies help provide information on metrics such as the number of visitors, bounce rate, traffic source, etc.

No cookies to display.

Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors.

No cookies to display.

Advertisement cookies are used to provide visitors with customized advertisements based on the pages you visited previously and to analyze the effectiveness of the ad campaigns.

No cookies to display.

Criterio di Leibniz serie

Home » Teoria serie numeriche » 📋 URL

Data una serie ss a segno alterno

s=∑n=n0∞(−1)n bns=\sum_{n=n_0}^{\infty}(-1)^n\,b_n

Supponiamo inoltre che

  • lim⁡n→+∞bn=0\displaystyle\lim_{n\to+\infty}b_n=0
  • {bn}\{b_n\} sia una successione monotona decrescente

Se tali condizioni sono verificate vale allora ss converge.

Nota bene: una successione si dice monotona decrescente se bn+1≤bnb_{n+1}\leq b_n a partire da un certo indice n≥nˉn\geq\bar{n} dove nˉ\bar{n} è un qualunque numero naturale arbitrariamente grande.

Nota bene: il criterio di Leibniz rappresenta una condizione sufficiente di convergenza valido solo per le serie di segno alterno.

Nota bene: nello studio di una serie a segno alterno conviene verificare in primo luogo la convergenza assoluta (generalmente è più facile), e solo nel caso in cui tale criterio non porti ad alcuna conclusione passare all’analisi tramite il criterio di Leibniz.

Questa pagina è stata utile?
SìNo
Torna in alto