What is the sum from n=0 to infinity of 2(1/(3^n)) ?

The sum from n=0 to infinity of 2(1/(3^n)) is 3

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sum from n=0 to infinity of 2(1/(3^n))

n = 0 \sum \infty 2 (\frac{1}{3 ^{n}})

3

Solution steps

n = 0 \sum \infty 2 \cdot \frac{1}{3 ^{n}}

Apply the constant multiplication rule:

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

= 2 \cdot n = 0 \sum \infty \frac{1}{3 ^{n}}

Apply Series Geometric Test:

\frac{3}{2}

= 2 \cdot \frac{3}{2}

Simplify

2 \cdot \frac{3}{2} : 3

= 3

\frac{d}{d z} (e^{z})

t a y l or sin (2 x - 1)

f (x) = arccot (x)

t an g e n t y = - 2 - 7 x^{2}, (3, - 65)

\frac{d}{d t} (t^{- 1})

What is the sum from n=0 to infinity of 2(1/(3^n)) ?
The sum from n=0 to infinity of 2(1/(3^n)) is 3