What is the sum from n=1 to infinity of 1/(n^2)+1/n ?

The sum from n=1 to infinity of 1/(n^2)+1/n is diverges

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sum from n=1 to infinity of 1/(n^2)+1/n

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

diverges

Solution steps

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

Apply Series Comparison Test:

diverges

= diverges

n = 0 \sum \infty \frac{6}{1 - n ^{2}}

n = 1 \sum \infty \frac{n - 1}{n 2 ^{n}}

n = 1 \sum \infty 9^{- n}

n = 2 \sum \infty (\frac{1}{4})^{n}

k = 2 \sum \infty \frac{1}{e ^{k}}

What is the sum from n=1 to infinity of 1/(n^2)+1/n ?
The sum from n=1 to infinity of 1/(n^2)+1/n is diverges