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

The sum from n=0 to infinity of 6/(5^n) is 15/2

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

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

\frac{15}{2}

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply Series Geometric Test:

\frac{5}{4}

= 6 \cdot \frac{5}{4}

Simplify

6 \cdot \frac{5}{4} : \frac{15}{2}

= \frac{15}{2}

\int 2 sec (2 x) tan (2 x) d x

y^{^{'}} + (\frac{1}{x}) y = 8 x^{2}

\int_{2}^{4} x^{2} y + y^{2} x + x + y d x

\frac{1}{1 + x ^{- 1}}

y^{^{''}} - 5 y^{^{'}} = 0, y (0) = 6, y^{^{'}} (0) = - 9

What is the sum from n=0 to infinity of 6/(5^n) ?
The sum from n=0 to infinity of 6/(5^n) is 15/2