Rekker: Konvergenstester

Hva er geometriske rekker?

En rekke $\sum a_n$ er geometrisk dersom hvert ledd er et multiplum av det forrige, dvs. $a_{n+1} = \textcolor{red}{r} a_n$ :

\textcolor{blue}{a} + \textcolor{blue}{a} \cdot \textcolor{red}{r} + \textcolor{blue}{a} \cdot \textcolor{red}{r} ^2 + \textcolor{blue}{a} \cdot \textcolor{red}{r} ^3 + \cdots = \sum_{n=1}^{\infty} \textcolor{blue}{a} \textcolor{red}{r} ^{n-1}

Hvis $|\textcolor{red}{r}| < 1$ konvergerer rekken og summen er:

S = \sum_{n = 1}^{\infty} \textcolor{blue}{a} \textcolor{red}{r} ^{n-1}= \frac{\textcolor{blue}{a}}{1-\textcolor{red}{r}}

Hvis $|\textcolor{red}{r}| \ge 1$ divergerer rekken.

👍🏼 Ros og ris 👎🏼

🛠️ Meld fra om feil 🛠️

📩 Send inn ønske 📩

Symboler:

★ Utfordring ★

Dypdykk

☰ Metode ☰

Bonus

Video