What is the sum from n=1 to infinity of 3/(5^{n+2)} ?

The sum from n=1 to infinity of 3/(5^{n+2)} is converges

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sum from n=1 to infinity of 3/(5^{n+2)}

n = 1 \sum \infty \frac{3}{5 ^{n + 2}}

converges

Solution steps

n = 1 \sum \infty \frac{3}{5 ^{n + 2}}

Apply the constant multiplication rule:

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

= 3 \cdot n = 1 \sum \infty \frac{1}{5 ^{n + 2}}

Apply Series Ratio Test:

converges

= 3 converges

= converges

n = 0 \sum \infty ln (1 - n^{2})

n = 0 \sum \infty 5^{- 2 n + 1} 3^{n}

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

n = 1 \sum \infty 4^{3 - 3 n}

k = 1 \sum \infty \frac{k}{2 ^{k - 1}}

What is the sum from n=1 to infinity of 3/(5^{n+2)} ?
The sum from n=1 to infinity of 3/(5^{n+2)} is converges