What is the sum from n=0 to infinity of 1/(7n+1) ?

The sum from n=0 to infinity of 1/(7n+1) is diverges

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sum from n=0 to infinity of 1/(7n+1)

n = 0 \sum \infty \frac{1}{7 n + 1}

diverges

Solution steps

n = 0 \sum \infty \frac{1}{7 n + 1}

Apply Series Integral Test:

diverges

= diverges

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

n = 0 \sum \infty \frac{1}{n 6 ^{n}}

k = 3 \sum \infty \frac{1}{k ^{2} + 5 k}

n = 1 \sum \infty \frac{9}{- 2 ^{n}}

n = 1 \sum \infty 45 (- 1)^{n}

What is the sum from n=0 to infinity of 1/(7n+1) ?
The sum from n=0 to infinity of 1/(7n+1) is diverges