What is the sum from n=0 to infinity of (2n)/(5n-3) ?

The sum from n=0 to infinity of (2n)/(5n-3) is diverges

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sum from n=0 to infinity of (2n)/(5n-3)

n = 0 \sum \infty \frac{2 n}{5 n - 3}

diverges

Solution steps

n = 0 \sum \infty \frac{2 n}{5 n - 3}

Apply the constant multiplication rule:

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

= 2 \cdot n = 0 \sum \infty \frac{n}{5 n - 3}

Factor

5 n - 3 : - (- 5 n + 3)

= 2 \cdot n = 0 \sum \infty \frac{n}{- ( - 5 n + 3 )}

Apply the constant multiplication rule:

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

= 2 (- n = 0 \sum \infty \frac{n}{- 5 n + 3})

Apply Series Divergence Test:

diverges

= 2 (- diverges)

= diverges

x = 1 \sum \infty x e^{- x^{2}}

n = 3 \sum \infty \frac{n}{5 ^{n}}

k = 1 \sum \infty k^{\frac{1}{k}}

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

n = 1 \sum \infty \frac{1}{n ^{3} - 5 n ^{2}}

What is the sum from n=0 to infinity of (2n)/(5n-3) ?
The sum from n=0 to infinity of (2n)/(5n-3) is diverges