What is the sum from n=1 to infinity of 5/(n^{0.6)} ?

The sum from n=1 to infinity of 5/(n^{0.6)} is diverges

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sum from n=1 to infinity of 5/(n^{0.6)}

n = 1 \sum \infty \frac{5}{n ^{0.6}}

diverges

Solution steps

n = 1 \sum \infty \frac{5}{n ^{0.6}}

Apply the constant multiplication rule:

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

= 5 \cdot n = 1 \sum \infty \frac{1}{n ^{0.6}}

Apply p-Series Test:

diverges

= 5 diverges

= diverges

n = 1 \sum \infty \frac{1}{4 n + 5}

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

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

n = 0 \sum \infty (\frac{2}{n})^{\frac{5}{n}}

n = 1 \sum \infty \frac{1}{3 n ^{2} + 7}

What is the sum from n=1 to infinity of 5/(n^{0.6)} ?
The sum from n=1 to infinity of 5/(n^{0.6)} is diverges