What is the sum from n=0 to infinity of (4n)/(8n+5) ?

The sum from n=0 to infinity of (4n)/(8n+5) is diverges

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sum from n=0 to infinity of (4n)/(8n+5)

n = 0 \sum \infty \frac{4 n}{8 n + 5}

diverges

Solution steps

n = 0 \sum \infty \frac{4 n}{8 n + 5}

Apply the constant multiplication rule:

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

= 4 \cdot n = 0 \sum \infty \frac{n}{8 n + 5}

Apply Series Divergence Test:

diverges

= 4 diverges

= diverges

\int_{1}^{2} \frac{ln ( x )}{x ^{3}} d x

\int \frac{1}{( \frac{1}{e ^{x}} + 1 )} d x

y = x^{2} - 5 x, (5, 0)

\frac{\partial}{\partial z} (y z^{2} - ln (x + z))

3 x^{6} - 6 x^{6} y^{7} + 4 x^{5} y^{4}

What is the sum from n=0 to infinity of (4n)/(8n+5) ?
The sum from n=0 to infinity of (4n)/(8n+5) is diverges