What is the sum from n=0 to infinity of 3^nx^{2n} ?

The sum from n=0 to infinity of 3^nx^{2n} is Radius of convergence is sqrt(1/3)

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sum from n=0 to infinity of 3^nx^{2n}

n = 0 \sum \infty 3^{n} x^{2 n}

Radius of convergence is \frac{1}{3}

Solution steps

n = 0 \sum \infty 3^{n} x^{2 n}

Use the Root Test to compute the convergence interval

Radius of convergence is \frac{1}{3}

\frac{1}{3} x^{3} - \frac{16}{x} - \frac{40}{3}

h \to 0 lim (7)

\int (8 x^{3} - 9 x^{2} + 4) d x

5 x - 1

\int \frac{( 1 - 2 x )}{x} d x

What is the sum from n=0 to infinity of 3^nx^{2n} ?
The sum from n=0 to infinity of 3^nx^{2n} is Radius of convergence is sqrt(1/3)