What is the sum from n=0 to infinity of (n^2)/(1+6n) ?

The sum from n=0 to infinity of (n^2)/(1+6n) is diverges

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sum from n=0 to infinity of (n^2)/(1+6n)

n = 0 \sum \infty \frac{n ^{2}}{1 + 6 n}

diverges

Solution steps

n = 0 \sum \infty \frac{n ^{2}}{1 + 6 n}

Apply Series Divergence Test:

diverges

= diverges

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

n = 1 \sum \infty (0.75)^{n - 1}

n = 1 \sum \infty \frac{3 ^{n}}{7 ^{n}}

n = 3 \sum \infty \frac{6}{n ^{3}}

n = 1 \sum \infty 4 (1.3)^{n}

What is the sum from n=0 to infinity of (n^2)/(1+6n) ?
The sum from n=0 to infinity of (n^2)/(1+6n) is diverges