What is the sum from n=1 to infinity of (n^2)/(n+5) ?

The sum from n=1 to infinity of (n^2)/(n+5) is diverges

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sum from n=1 to infinity of (n^2)/(n+5)

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

diverges

Solution steps

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

Apply Series Divergence Test:

diverges

= diverges

\int_{0}^{π} tan (x) d x

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

\int \frac{tan ( x ) - 1}{sec ^{2} ( x )} d x

cos (x) y^{^{'}} + y sin (x) = 1

\int cos^{4} (5 x + 8) d x

What is the sum from n=1 to infinity of (n^2)/(n+5) ?
The sum from n=1 to infinity of (n^2)/(n+5) is diverges