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

The sum from n=1 to infinity of ((cos(pi))/3)^n is converges

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sum from n=1 to infinity of ((cos(pi))/3)^n

n = 1 \sum \infty (\frac{cos ( π )}{3})^{n}

converges

Solution steps

n = 1 \sum \infty (\frac{cos ( π )}{3})^{n}

\frac{cos ( π )}{3} = - \frac{1}{3}

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

Apply Series Ratio Test:

converges

= converges

\int_{0}^{\frac{π}{4}} sin^{3} (x) d x

\frac{\partial}{\partial y} (\frac{2 x}{x ^{2} + y})

16 y^{^{''}} + 8 y^{^{'}} + y = x + 6

\frac{d y}{d x} = (\frac{x y + 3 x - y - 3}{x y - 2 x + 4 y - 8})

y (x + 5) + y^{^{'}} = 0

What is the sum from n=1 to infinity of ((cos(pi))/3)^n ?
The sum from n=1 to infinity of ((cos(pi))/3)^n is converges