What is the sum from n=1 to infinity of (n+6)/(n^2) ?

The sum from n=1 to infinity of (n+6)/(n^2) is diverges

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sum from n=1 to infinity of (n+6)/(n^2)

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

diverges

Solution steps

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

Apply Series Comparison Test:

diverges

= diverges

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

k = 2 \sum \infty \frac{k}{ln ( k )}

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

n = 8 \sum \infty \frac{1}{n ^{2} + 64}

n = 1 \sum \infty \frac{1}{3 ( 2 ^{n} )}

What is the sum from n=1 to infinity of (n+6)/(n^2) ?
The sum from n=1 to infinity of (n+6)/(n^2) is diverges