What is the sum from n=0 to infinity of 1/n-1/(n^2) ?

The sum from n=0 to infinity of 1/n-1/(n^2) is diverges

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sum from n=0 to infinity of 1/n-1/(n^2)

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

diverges

Solution steps

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

Apply Series Limit Comparison Test:

diverges

= diverges

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

n = 1 \sum \infty (- \frac{5}{6})^{n}

n = 1 \sum \infty \frac{9 n ^{2}}{n !}

n = 2 \sum \infty \frac{3}{( n ( n + 3 ) )}

k = 1 \sum \infty (cos (6))^{k}

What is the sum from n=0 to infinity of 1/n-1/(n^2) ?
The sum from n=0 to infinity of 1/n-1/(n^2) is diverges