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

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

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

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

diverges

Solution steps

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

Factor

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

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

Apply the constant multiplication rule:

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

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

Apply Series Divergence Test:

diverges

= - diverges

= diverges

n = 1 \sum \infty (2)^{n}

n = 0 \sum \infty 8 - 5 n^{4}

n = 1 \sum \infty \frac{n !}{1 2 ^{n}}

n = 0 \sum \infty \frac{n ^{2}}{7 ^{n}}

k = 1 \sum \infty (\frac{1}{4})^{k}

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