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

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

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

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

diverges

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply Series Comparison Test:

diverges

= 3 diverges

= diverges

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

n = 0 \sum \infty ln (\frac{1}{n})

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

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

n = 5 \sum \infty ln (1 + \frac{1}{n})

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