What is the sum from n=0 to infinity of 2*0.3^n ?

The sum from n=0 to infinity of 2*0.3^n is 2.85714…

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sum from n=0 to infinity of 2*0.3^n

n = 0 \sum \infty 2 \cdot 0. 3^{n}

2.85714 \dots

Solution steps

n = 0 \sum \infty 2 \cdot 0. 3^{n}

Apply the constant multiplication rule:

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

= 2 \cdot n = 0 \sum \infty 0. 3^{n}

Apply Series Geometric Test:

1.42857 \dots

= 2 \cdot 1.42857 \dots

Simplify

= 2.85714 \dots

\frac{d y}{d x} + x (y^{2} + y) = 0

\int \frac{2 tan ( x )}{1 - tan ^{2} ( x )} d x

\frac{d}{d x} (tan (2 x + 1))

y = x^{3} + 6 x

4 + x^{6}

What is the sum from n=0 to infinity of 2*0.3^n ?
The sum from n=0 to infinity of 2*0.3^n is 2.85714…