What is the sum from n=0 to infinity of 5*(1/4)^n ?

The sum from n=0 to infinity of 5*(1/4)^n is 20/3

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sum from n=0 to infinity of 5*(1/4)^n

n = 0 \sum \infty 5 \cdot (\frac{1}{4})^{n}

\frac{20}{3}

Solution steps

n = 0 \sum \infty 5 (\frac{1}{4})^{n}

Apply the constant multiplication rule:

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

= 5 \cdot n = 0 \sum \infty (\frac{1}{4})^{n}

Apply Series Geometric Test:

\frac{4}{3}

= 5 \cdot \frac{4}{3}

Simplify

5 \cdot \frac{4}{3} : \frac{20}{3}

= \frac{20}{3}

n = 0 \sum \infty \frac{n}{n !}

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

n = 1 \sum \infty \frac{e ^{n}}{n ^{4}}

n = 1 \sum \infty \frac{4}{n ^{2} + 4 n + 3}

n = 5 \sum \infty cos (\frac{1}{n})

What is the sum from n=0 to infinity of 5*(1/4)^n ?
The sum from n=0 to infinity of 5*(1/4)^n is 20/3