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

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

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

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

diverges

Solution steps

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

Apply Series Divergence Test:

diverges

= diverges

n = 0 \sum \infty \frac{- 1}{n ^{2}}

n = 1 \sum \infty \frac{6}{3 n + 2}

n = 4 \sum \infty \frac{e ^{- n} + 1}{n}

n = 0 \sum \infty \frac{6}{n ( n + 2 )}

k = 1 \sum \infty \frac{k}{k ^{2} - 1}

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