What is the sum from n=1 to infinity of (2n^3)/(n^4) ?

The sum from n=1 to infinity of (2n^3)/(n^4) is diverges

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sum from n=1 to infinity of (2n^3)/(n^4)

n = 1 \sum \infty \frac{2 n ^{3}}{n ^{4}}

diverges

Solution steps

n = 1 \sum \infty \frac{2 n ^{3}}{n ^{4}}

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= 2 \cdot n = 1 \sum \infty \frac{n ^{3}}{n ^{4}}

Simplify

\frac{n ^{3}}{n ^{4}} : \frac{1}{n}

= 2 \cdot n = 1 \sum \infty \frac{1}{n}

Apply Cauchy's Convergence Condition:

diverges

= 2 diverges

= diverges

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

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

n = 1 \sum \infty \frac{2 n + 3}{n + 1}

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

n = 0 \sum \infty 2 (\frac{1}{3})^{n}

What is the sum from n=1 to infinity of (2n^3)/(n^4) ?
The sum from n=1 to infinity of (2n^3)/(n^4) is diverges