What is the sum from n=0 to infinity of (2n)/(3n+1) ?

The sum from n=0 to infinity of (2n)/(3n+1) is diverges

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sum from n=0 to infinity of (2n)/(3n+1)

n = 0 \sum \infty \frac{2 n}{3 n + 1}

diverges

Solution steps

n = 0 \sum \infty \frac{2 n}{3 n + 1}

Apply the constant multiplication rule:

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

= 2 \cdot n = 0 \sum \infty \frac{n}{3 n + 1}

Apply Series Divergence Test:

diverges

= 2 diverges

= diverges

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\int \frac{1}{3 - y} d y

What is the sum from n=0 to infinity of (2n)/(3n+1) ?
The sum from n=0 to infinity of (2n)/(3n+1) is diverges