What is the sum from n=0 to infinity of 1/2 (1/2)^n ?

The sum from n=0 to infinity of 1/2 (1/2)^n is 1

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sum from n=0 to infinity of 1/2 (1/2)^n

n = 0 \sum \infty \frac{1}{2} (\frac{1}{2})^{n}

1

Solution steps

n = 0 \sum \infty \frac{1}{2} (\frac{1}{2})^{n}

Apply the constant multiplication rule:

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

= \frac{1}{2} \cdot n = 0 \sum \infty (\frac{1}{2})^{n}

Apply Series Geometric Test:

2

= \frac{1}{2} \cdot 2

Simplify

\frac{1}{2} \cdot 2 : 1

= 1

\int \frac{2 x + 3}{x ^{2} + 1} d x

x \to 4 - lim (16 - x^{2})

\frac{d y}{d x}, 1 = (\frac{y}{x})

f (x) = 8 cos (t)

x \to 16 lim (\frac{sin ( x )}{x})

What is the sum from n=0 to infinity of 1/2 (1/2)^n ?
The sum from n=0 to infinity of 1/2 (1/2)^n is 1