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3 years ago

14

i am sorry but how do we give brainlest cause i do not know and i am a beginner and this is not math i just want to give brainle

st to the people who answered my question

1 answer:

pychu [463]3 years ago

5 0

Answer:

click the crown icon in any of two answers

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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

Alona [7]

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

#SPJ4

8 0

2 years ago

Graph both functions to find the solution(s) to the system.

konstantin123 [22]

graphed it with desmos (free as app and website).

the solutions are in the screenshot

(1, 3)

(3, 7)

5 0

3 years ago

And this one too!! Thanks in advance

Harlamova29_29 [7]

Answer:

20/9 sq.feet

Step-by-step explanation:

The width is 4/3 ft because 1/3 times 4 is 4/3 and the length is 5/3 because 1/3 times 5 is 5/3.

Then to find the area you do length times width.

5/3 ×4/3= 20/9 sq. feet

I hope this helps! :)

3 0

4 years ago

The image of -4,6 reflected along the y axis is?

mr_godi [17]

The image of the point is still a point. The reflection point across the y-axis is (4,6)

4 0

4 years ago

Roby spent two months traveling in country A. The day she arrived, the exchange rate was 1.3 country A dollars per country B. Co

Fantom [35]

Answer:

650 Country A Dollars

Step-by-step explanation:

1 Country B Dollar = 1.3 Country A Dollar

Country A Dollars for 500 Country B Dollars = 500 x 1.3 = 650

8 0

3 years ago