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

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

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

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

diverges

Solution steps

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

Apply Series Divergence Test:

diverges

= diverges

k = 0 \sum \infty (\frac{1}{2})^{k}

n = 0 \sum \infty \frac{10 n}{4 n + 1}

n = 1 \sum \infty \frac{9}{5 n ^{3}}

n = 0 \sum \infty \frac{n}{1}

n = 0 \sum \infty \frac{4}{n}

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