What is the sum from n=1 to infinity of (7n)/(5+6n) ?

The sum from n=1 to infinity of (7n)/(5+6n) is diverges

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sum from n=1 to infinity of (7n)/(5+6n)

n = 1 \sum \infty \frac{7 n}{5 + 6 n}

diverges

Solution steps

n = 1 \sum \infty \frac{7 n}{5 + 6 n}

Apply the constant multiplication rule:

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

= 7 \cdot n = 1 \sum \infty \frac{n}{5 + 6 n}

Apply Series Divergence Test:

diverges

= 7 diverges

= diverges

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

n = 1 \sum \infty \frac{n ^{3}}{8 ^{n}}

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

n = 3 \sum \infty \frac{1}{n ^{100}}

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

What is the sum from n=1 to infinity of (7n)/(5+6n) ?
The sum from n=1 to infinity of (7n)/(5+6n) is diverges