What is the sum from n=1 to infinity of 7/(pi^n) ?

The sum from n=1 to infinity of 7/(pi^n) is converges

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sum from n=1 to infinity of 7/(pi^n)

n = 1 \sum \infty \frac{7}{π ^{n}}

converges

Solution steps

n = 1 \sum \infty \frac{7}{π ^{n}}

Apply the constant multiplication rule:

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

= 7 \cdot n = 1 \sum \infty \frac{1}{π ^{n}}

Apply Series Ratio Test:

converges

= 7 converges

= converges

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

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

n = 1 \sum \infty arccos (\frac{1}{n})

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

n = 2 \sum \infty (\frac{1}{3})^{2 n}

What is the sum from n=1 to infinity of 7/(pi^n) ?
The sum from n=1 to infinity of 7/(pi^n) is converges