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3 years ago

can someone please help me with this??? and please provide an example if possible! thank you so much!

Mathematics

1 answer:

aleksklad [387]3 years ago

4 0

Answer:

a point in geometry is a location, has no size, no length, no depth. a point is shown like a dot.

a line : is a line of points that extents infinity in two direction, it has one dimension which is length ( tape)

a line segment : is a part of a line that defines by two points.( board game made of four line) segments

plane:A plane extends infinitely in two dimensions. It has no thickness( ceiling, roof of the house, sheet of paper)

an angle : an angle is the figure formed by two rays, ( example the edge of a table)

( you can add examples from your house)

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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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2 years ago

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3 years ago

Please help me with this

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Answer:

a = 5

Step-by-step explanation:

If it's easier for you, you can replace n(a) with y and put a as x.

Now the equation is y = 7x + 4.

It asks you to put in 39 as y.

39 = 7x + 4.

To solve this, the goal is to isolate the variable on one side. The first step I see is to subtract the 4 from both sides.

35 = 7x

Now divide both sides by 7 and we're done!

5 = x

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