What is the sum from n=0 to infinity of 1/(1-n) ?

The sum from n=0 to infinity of 1/(1-n) is diverges

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sum from n=0 to infinity of 1/(1-n)

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

diverges

Solution steps

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

Factor

1 - n : - (- 1 + n)

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

Apply the constant multiplication rule:

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

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

Apply Series Comparison Test:

diverges

= - diverges

= diverges

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

n = 1 \sum \infty \frac{5}{4 ^{n} - 3 ^{n}}

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

n = 0 \sum \infty 3^{n} 4^{- n + 1}

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

What is the sum from n=0 to infinity of 1/(1-n) ?
The sum from n=0 to infinity of 1/(1-n) is diverges