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3 years ago

Three less than n equals 2 (solve for n)

Mathematics

2 answers:

ladessa [460]3 years ago

7 0

If three less than 'n' equals 2, 'n'=5

3+2=5

borishaifa [10]3 years ago

4 0

The answer is 5 !!!!!!!!

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Eddi Din [679]

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3 years ago

Read 2 more answers

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

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2 years ago

A playground is located on a triangular piece of land. Two sides of the playground are 157 feet long and they meet at an angle o

jok3333 [9.3K]

Answer:

$5,671.84

Step-by-step explanation:

To find the third side, we can use the law of cosines:

c^2 = a^2 + b^2 - 2ab*cos(theta)

c^2 = 157^2 + 157^2 - 2*157*157*cos(65)

c^2 = 28463.7649

c = 168.71 feet

The perimeter of the playground is:

P = 157 + 157 + 168.71 = 482.71 feet

If each foot costs $11.75, the final cost is:

Cost = 482.71 * 11.75 = $5,671.84

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3 years ago

Describe methods you can use to show a proportional relationship between two variables ,x and y. Each method, explains how you c

ivann1987 [24]

Answer: Find answer and explanation in the attached document.

Step-by-step explanation:

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4 years ago

A student is trying to solve the system of two equations given below:

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Answer:

Step-by-step explanation:

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3 years ago