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

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

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

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

diverges

Solution steps

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

Apply Series Integral Test:

diverges

= diverges

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

n = 1 \sum \infty \frac{2}{n ^{5}}

n = 2 \sum \infty \frac{3}{n ^{2} - n}

n = 1 \sum \infty (\frac{3}{4})^{- n}

n = 2 \sum \infty (\frac{3}{7})^{3 n}

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