What is the sum from k=0 to infinity of (1/2)^{2k+1} ?

The sum from k=0 to infinity of (1/2)^{2k+1} is converges

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sum from k=0 to infinity of (1/2)^{2k+1}

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

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What is the sum from k=0 to infinity of (1/2)^{2k+1} ?
The sum from k=0 to infinity of (1/2)^{2k+1} is converges