What is the sum from n=10 to infinity of 3/(n^{4.6)} ?

The sum from n=10 to infinity of 3/(n^{4.6)} is converges

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sum from n=10 to infinity of 3/(n^{4.6)}

n = 10 \sum \infty \frac{3}{n ^{4.6}}

converges

Solution steps

n = 10 \sum \infty \frac{3}{n ^{4.6}}

Apply the constant multiplication rule:

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

= 3 \cdot n = 10 \sum \infty \frac{1}{n ^{4.6}}

Apply p-Series Test:

converges

= 3 converges

= converges

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

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

n = 1 \sum \infty n (\frac{2}{5})^{n}

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

n = 0 \sum \infty \frac{8}{5 - n}

What is the sum from n=10 to infinity of 3/(n^{4.6)} ?
The sum from n=10 to infinity of 3/(n^{4.6)} is converges