What is the sum from n=0 to infinity of 5/n ?

The sum from n=0 to infinity of 5/n is diverges

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sum from n=0 to infinity of 5/n

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

diverges

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply Cauchy's Convergence Condition:

diverges

= 5 diverges

= diverges

n = 1 \sum \infty \frac{8}{5 n + 12}

n = 0 \sum \infty \frac{2}{9 ^{n}}

n = 1 \sum \infty \frac{n}{3 n - 1}

n = 0 \sum \infty (- \frac{1}{8})^{n}

n = 1 \sum \infty 8 ln (\frac{n}{n + 1})

What is the sum from n=0 to infinity of 5/n ?
The sum from n=0 to infinity of 5/n is diverges