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

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

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

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

diverges

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply Series Integral Test:

diverges

= 2 diverges

= diverges

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

n = 0 \sum \infty 8 + 4 + 2 + 1

n = 1 \sum \infty (- \frac{9}{8})^{n - 1}

n = 0 \sum \infty \frac{1}{1 + 3 n ^{4}}

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

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