What is the sum from n=0 to infinity of (-1^n)/(5^n) ?

The sum from n=0 to infinity of (-1^n)/(5^n) is converges

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sum from n=0 to infinity of (-1^n)/(5^n)

n = 0 \sum \infty \frac{- 1 ^{n}}{5 ^{n}}

converges

Solution steps

n = 0 \sum \infty \frac{- 1 ^{n}}{5 ^{n}}

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= - n = 0 \sum \infty \frac{1 ^{n}}{5 ^{n}}

Apply Series Ratio Test:

converges

= - converges

= converges

n = 0 \sum \infty \frac{1}{3 ^{2 n + 1}}

n = 0 \sum \infty \frac{6 ^{n}}{5 ^{n}}

n = 1 \sum \infty \frac{1}{2 n + 9}

n = 1 \sum \infty n^{9} (1 + n^{10})

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

What is the sum from n=0 to infinity of (-1^n)/(5^n) ?
The sum from n=0 to infinity of (-1^n)/(5^n) is converges