What is the sum from n=1 to infinity of (n+3)/(2n+1) ?

The sum from n=1 to infinity of (n+3)/(2n+1) is diverges

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sum from n=1 to infinity of (n+3)/(2n+1)

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

diverges

Solution steps

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

Apply Series Divergence Test:

diverges

= diverges

k = 0 \sum \infty (- \frac{1}{5})^{k}

n = 1 \sum \infty \frac{8 - 5}{n ^{2}}

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

n = 1 \sum \infty \frac{5}{17 + 8 ^{n}}

n = 2 \sum \infty \frac{1}{6} (\frac{5}{6})^{n}

What is the sum from n=1 to infinity of (n+3)/(2n+1) ?
The sum from n=1 to infinity of (n+3)/(2n+1) is diverges