What is the sum from n=1 to infinity of (2n)/(9n+1) ?

The sum from n=1 to infinity of (2n)/(9n+1) is diverges

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sum from n=1 to infinity of (2n)/(9n+1)

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

diverges

Solution steps

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

Apply the constant multiplication rule:

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

= 2 \cdot n = 1 \sum \infty \frac{n}{9 n + 1}

Apply Series Divergence Test:

diverges

= 2 diverges

= diverges

n = 0 \sum \infty 5 n^{3} + n

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

k = 3 \sum \infty \frac{9}{k ln ^{2} ( k )}

n = 0 \sum \infty 1 e^{- 5 n}

n = 0 \sum \infty (\frac{8}{5})^{n}

What is the sum from n=1 to infinity of (2n)/(9n+1) ?
The sum from n=1 to infinity of (2n)/(9n+1) is diverges