What is the sum from k=2 to infinity of (-0.5)^k ?

The sum from k=2 to infinity of (-0.5)^k is converges

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sum from k=2 to infinity of (-0.5)^k

k = 2 \sum \infty (- 0.5)^{k}

converges

Solution steps

k = 2 \sum \infty (- 0.5)^{k}

Apply Series Ratio Test:

converges

= converges

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

n = 0 \sum \infty n^{4}

n = 0 \sum \infty n^{9}

n = 1 \sum \infty \frac{3 n}{3 + n ^{3}}

n = 1 \sum \infty (0.5)^{n - 1}

What is the sum from k=2 to infinity of (-0.5)^k ?
The sum from k=2 to infinity of (-0.5)^k is converges