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

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

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

n = 0 \sum \infty \frac{3}{2 n + 2}

diverges

Solution steps

n = 0 \sum \infty \frac{3}{2 n + 2}

Apply the constant multiplication rule:

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

= 3 \cdot n = 0 \sum \infty \frac{1}{2 n + 2}

Apply Series Integral Test:

diverges

= 3 diverges

= diverges

n = 1 \sum \infty n^{- 5}

n = 3 \sum \infty \frac{1}{n ^{2} - 4}

n = 1 \sum \infty n (\frac{1}{3})^{n - 1}

n = 1 \sum \infty (\frac{2}{13})^{n}

n = 1 \sum \infty n^{- n}

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