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

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

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

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

2 + 2

Solution steps

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

Simplify

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

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

Apply Series Geometric Test:

2 + 2

= 2 + 2

n = 0 \sum \infty (0.3)^{n}

n = 0 \sum \infty (1 + \frac{2}{5 n})^{n}

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}

What is the sum from n=0 to infinity}sqrt(2 of ^{-n) ?
The sum from n=0 to infinity}sqrt(2 of ^{-n) is 2+sqrt(2)