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

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

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

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

diverges

Solution steps

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

Factor

1 - 2 n : - (- 1 + 2 n)

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

Apply the constant multiplication rule:

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

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

Apply Series Comparison Test:

diverges

= - diverges

= diverges

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