What is the sum from k=1 to infinity of 5/k ?

The sum from k=1 to infinity of 5/k is diverges

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sum from k=1 to infinity of 5/k

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

diverges

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply Cauchy's Convergence Condition:

diverges

= 5 diverges

= diverges

n = 0 \sum \infty \frac{1}{6 - n}

n = 1 \sum \infty 6^{\frac{1}{n}}

n = 1 \sum \infty 6 (0.8)^{n - 1}

n = 1 \sum \infty (cos (21))^{n}

What is the sum from k=1 to infinity of 5/k ?
The sum from k=1 to infinity of 5/k is diverges