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

The sum from n=0 to infinity of (((-1)^n)/(2^n))x^{2n} is Radius of convergence is sqrt(2)

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sum from n=0 to infinity of (((-1)^n)/(2^n))x^{2n}

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

Radius of convergence is 2

Solution steps

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

Use the Root Test to compute the convergence interval

Radius of convergence is 2

\frac{d y}{d x} = x (x - 2)

ln (6 x)

(x + y + 4 d x) + (2 x + 2 y + 1 d y) = 0

f (x) = 4 e^{x} + x, (0, 4)

\frac{\partial}{\partial x} (\frac{1}{3} t^{6} - 6 t^{4} + t)

What is the sum from n=0 to infinity of (((-1)^n)/(2^n))x^{2n} ?
The sum from n=0 to infinity of (((-1)^n)/(2^n))x^{2n} is Radius of convergence is sqrt(2)