What is the sum from n=2 to infinity of n^2-n ?

The sum from n=2 to infinity of n^2-n is diverges

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sum from n=2 to infinity of n^2-n

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

diverges

Solution steps

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

Multiply by the conjugate of

n^{2} - n : \frac{n ^{4} - n ^{2}}{n ^{2} + n}

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

Simplify

\frac{n ^{4} - n ^{2}}{n ^{2} + n} : n (n - 1)

= n = 2 \sum \infty n (n - 1)

Apply Series Divergence Test:

diverges

= diverges

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