What is the sum from n=1 to infinity of (-9)^{-n} ?

The sum from n=1 to infinity of (-9)^{-n} is converges

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sum from n=1 to infinity of (-9)^{-n}

n = 1 \sum \infty (- 9)^{- n}

converges

Solution steps

n = 1 \sum \infty (- 9)^{- n}

Apply Series Ratio Test:

converges

= converges

k = 0 \sum \infty (\frac{1}{5})^{k}

n = 1 \sum \infty \frac{1}{3 n ^{4} + 4}

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

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

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

What is the sum from n=1 to infinity of (-9)^{-n} ?
The sum from n=1 to infinity of (-9)^{-n} is converges