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

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

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

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

diverges

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply Series Comparison Test:

diverges

= 2 diverges

= diverges

\frac{d}{d x} (\frac{1 - 3 x ^{2}}{1 - 2 x})

\frac{d}{d x} (9 x + 5)

x \to 5 - lim (\frac{1}{( x - 5 ) ^{2}})

10

f (x) = (x + 1)^{\frac{1}{2}}

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