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

The sum from n=3 to infinity of ((-1)/2)^n is -1/12

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

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

- \frac{1}{12}

Solution steps

n = 3 \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}

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

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

= \frac{2}{3} - (\frac{- 1}{2})^{0} - (\frac{- 1}{2})^{1} - (\frac{- 1}{2})^{2}

Simplify

\frac{2}{3} - (\frac{- 1}{2})^{0} - (\frac{- 1}{2})^{1} - (\frac{- 1}{2})^{2} : - \frac{1}{12}

= - \frac{1}{12}

y^{^{''}} + 10 y^{^{'}} + 26 y = 0

f (x) = x^{2} 9 - x^{2}

\frac{d}{d x} ((sin (\frac{x}{2}) - cos (\frac{x}{2}))^{2})

cos (x), sin (x), 0, \frac{π}{2}

\frac{d y}{d x} = 10 y \cdot e^{x + 7}

What is the sum from n=3 to infinity of ((-1)/2)^n ?
The sum from n=3 to infinity of ((-1)/2)^n is -1/12