sum from n=0 to infinity}sqrt(2 of ^{-n)

Lösung

n = 0 \sum \infty 2^{- n}

2 + 2

Dezimale

3.41421 \dots

Schritte zur Lösung

n = 0 \sum \infty (2)^{- n}

Vereinfache

(2)^{- n} : \frac{1}{( 2 ) ^{n}}

= n = 0 \sum \infty \frac{1}{( 2 ) ^{n}}

Geometrischen Test der Reihe anwenden:

2 + 2

= 2 + 2

n = 1 \sum \infty \frac{n}{2 n ^{2} - 3}

n = 0 \sum \infty (\frac{7}{9})^{n}

n = 0 \sum \infty \frac{( n + 1 )}{n}

k = 1 \sum \infty k e^{- 6 k^{2}}

n = 2 \sum \infty \frac{1}{n} - \frac{1}{n + 2}