What is the sum from n=0 to infinity of 1/(1/n) ?

The sum from n=0 to infinity of 1/(1/n) is diverges

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sum from n=0 to infinity of 1/(1/n)

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

diverges

Solution steps

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

Simplify

= n = 1 \sum \infty n

Apply Series Divergence Test:

diverges

= diverges

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

n = 1 \sum \infty \frac{1}{n + 9 ^{n}}

n = 0 \sum \infty \frac{9}{10}

n = 2 \sum \infty 4 n^{- 2}

n = 0 \sum \infty (\frac{1}{13})^{n}

What is the sum from n=0 to infinity of 1/(1/n) ?
The sum from n=0 to infinity of 1/(1/n) is diverges