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2 years ago

Can you explain clearly. This is very hard for me.

Mathematics

1 answer:

Crazy boy [7]2 years ago

6 0

The answer to the question is 6 yards and 2 feet

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Find the radius of convergence, then determine the interval of convergence

galben [10]

The radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series. This can be obtained by using ratio test.

<h3>Find the radius of convergence R and the interval of convergence:</h3>

Ratio test is the test that is used to find the convergence of the given power series.

First aₙ is noted and then aₙ₊₁ is noted.

For ∑ aₙ, aₙ and aₙ₊₁ is noted.

$\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|$ = β

If β < 1, then the series converges

If β > 1, then the series diverges

If β = 1, then the series inconclusive

Here $a_{k}$ = $\frac{(x+2)^{k}}{\sqrt{k} }$ and $a_{k+1}$ = $\frac{(x+2)^{k+1}}{\sqrt{k+1} }$

Now limit is taken,

$\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|$ = $\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }/\frac{(x+2)^{k} }{\sqrt{k} }|$

= $\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }\frac{\sqrt{k} }{(x+2)^{k}}|$

= $\lim_{n \to \infty} |{(x+2) } }{\sqrt{\frac{k}{k+1} } }}|$

= $|{x+2 }|\lim_{n \to \infty}}{\sqrt{\frac{k}{k+1} } }}$

= $|{x+2 }|$ < 1

- 1 < ${x+2 }$ < 1

- 1 - 2 < x < 1 - 2

- 3 < x < - 1

We get that,

interval of convergence = (-3, -1)

radius of convergence R = 1

Hence the radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series.

Learn more about radius of convergence here:

brainly.com/question/14394994

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6 months ago

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What is a tree diagram? can you make one?

liberstina [14]

DescriptionIn probability theory, a tree diagram may be used to represent a probability space. Tree diagrams may represent a series of independent events or conditional probabilities. Each node on the diagram represents an event and is associated with the probability of that event. You can make one.

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2 years ago

Help me with this question

mart [117]

Answer:

40 in.

Step-by-step explanation:

hope it helps

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Triangle ABC is shown in the diagram below. Show two different ways that you can determine the measure of ABC

iragen [17]

Step-by-step explanation:

vertical angles or line pairs

c=60

180-120=60

180-131=49

60+49=109

180-109=71

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Select the statement that represents all the solutions of the inequality. d < 7 all rational numbers equal to 7 all integers

Paraphin [41]

Aspongebob at the bottom of the sea

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In a plain, robust, conversational style, the author known as “Elena Ferrante” has captivated readers worldwide with her chronicle of a complicated friendship between two women.

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