What is the sum from n=0 to infinity of 4/(7^n) ?

The sum from n=0 to infinity of 4/(7^n) is 14/3

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sum from n=0 to infinity of 4/(7^n)

n = 0 \sum \infty \frac{4}{7 ^{n}}

\frac{14}{3}

Decimal

4.66666 \dots

Solution steps

n = 0 \sum \infty \frac{4}{7 ^{n}}

Apply the constant multiplication rule:

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

= 4 \cdot n = 0 \sum \infty \frac{1}{7 ^{n}}

Apply Series Geometric Test:

\frac{7}{6}

= 4 \cdot \frac{7}{6}

Simplify

4 \cdot \frac{7}{6} : \frac{14}{3}

= \frac{14}{3}

\int tan (x) (sec (x))^{2} d x

\frac{d}{d x} (e^{4 y - x^{2} - y^{2}})

\int_{\frac{π}{4}}^{\infty} \frac{7}{x} d x

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

\frac{d}{d x} (x^{n})

What is the sum from n=0 to infinity of 4/(7^n) ?
The sum from n=0 to infinity of 4/(7^n) is 14/3