What is the sum from n=0 to infinity of 1/6 (5/6)^n ?

The sum from n=0 to infinity of 1/6 (5/6)^n is 1

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sum from n=0 to infinity of 1/6 (5/6)^n

n = 0 \sum \infty \frac{1}{6} (\frac{5}{6})^{n}

1

Solution steps

n = 0 \sum \infty \frac{1}{6} (\frac{5}{6})^{n}

Apply the constant multiplication rule:

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

= \frac{1}{6} \cdot n = 0 \sum \infty (\frac{5}{6})^{n}

Apply Series Geometric Test:

6

= \frac{1}{6} \cdot 6

Simplify

\frac{1}{6} \cdot 6 : 1

= 1

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

n = 1 \sum \infty \frac{10 0 ^{n}}{n !}

n = 1 \sum \infty n ln (n)

k = 2 \sum \infty \frac{1}{k ^{2} - 1}

n = 0 \sum \infty \frac{cos ( nπ )}{n}

What is the sum from n=0 to infinity of 1/6 (5/6)^n ?
The sum from n=0 to infinity of 1/6 (5/6)^n is 1