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

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

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

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

2

Solution steps

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

Apply the constant multiplication rule:

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

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

n = k \sum \infty (a_{n}) = n = 0 \sum \infty (a_{n}) - a_{0} - a_{1} - \dots a_{k - 1}

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

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

= 2 (2 - \frac{1}{2 ^{0}})

Simplify

= 2

\int x (sin^{2} (x)) d x

2 y^{^{''}} + 16 y^{^{'}} + 32 y = 0, y (0) = - 3, y^{^{'}} (0) = 10

\frac{d}{d x} (f (x) (x)^{3} (x))

f (x) = cos (2 x)

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