What is the sum from n=0 to infinity of 3(1/11)^n ?

The sum from n=0 to infinity of 3(1/11)^n is 33/10

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sum from n=0 to infinity of 3(1/11)^n

n = 0 \sum \infty 3 (\frac{1}{11})^{n}

\frac{33}{10}

Solution steps

n = 0 \sum \infty 3 (\frac{1}{11})^{n}

Apply the constant multiplication rule:

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

= 3 \cdot n = 0 \sum \infty (\frac{1}{11})^{n}

Apply Series Geometric Test:

\frac{11}{10}

= 3 \cdot \frac{11}{10}

Simplify

3 \cdot \frac{11}{10} : \frac{33}{10}

= \frac{33}{10}

n = 1 \sum \infty (- \frac{6}{8})^{n - 1}

n = 0 \sum \infty \frac{1}{1 - 5 n}

n = 1 \sum \infty (\frac{3}{7})^{n - 1}

n = 6 \sum \infty \frac{1}{n} - \frac{1}{n + 2}

n = 0 \sum \infty c n

What is the sum from n=0 to infinity of 3(1/11)^n ?
The sum from n=0 to infinity of 3(1/11)^n is 33/10