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Elenna [48]
3 years ago
15

If a triangle has a 30° angle and a 60° angle, then the hypotenuse of the triangle is twice the

Mathematics
1 answer:
Dimas [21]3 years ago
5 0
I believe it’s false, sorry if I’m wrong
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Find the radius of convergence of the power series. (if you need to use or –, enter infinity or –infinity, respectively. ) [infi
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For given power series \sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n} the radius of convergence is 2.

For given question,

We have been given a power series \sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n}

We need to find the radius of convergence of the power series.

We use ratio test to find the radius of convergence of the power series.

Let a_n=\frac{(-1)^nx^n}{2^n}

\Rightarrow a_{n+1}=\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}

Consider,

\lim_{n \to \infty}|\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}}{ \frac{(-1)^nx^n}{2^n} } |\\\\=\lim_{n \to \infty} |\frac{(-1)^{n+1}x^{n+1}}{2^{n+1}}\times \frac{2^n}{(-1)^nx^n} |\\\\=\lim_{n \to \infty} |\frac{(-1)x}{2} |\\\\=\lim_{n \to \infty}|\frac{-x}{2} |\\\\=\frac{x}{2}

By Ratio test, given power series converges at |\frac{x}{2} | < 1

⇒ |x| < 2

So, the radius of convergence is 2.

Therefore, for given power series \sum_{n=0}^{\infty} \frac{(-1)^nx^n}{2^n} the radius of convergence is 2.

Learn more about the radius of convergence here:

brainly.com/question/2289050

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Marco buys a certain brand of shampoo from a supplier at $7.25 per bottle. He sells it to his customer at a markup of 25%. What
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Multiply 7.25 × .25.

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