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determine whether the series is absolutely convergent, conditionally convergent, or divergent sin(n)/3^n convergent

Answers

Answer 1

Answer:

Answer:

absolutely convergent

Step-by-step explanation:

given data

sin(n)/3^n

solution

we have given term $(sin(n))/(3^n)$

when n = 1

and we know that

value of sin(n) ≤ 1

so that we can say that

$(sin(n))/(3^n)$ ≤ $(1)/(3^n)$ or $((1)/(3))^n$

here $(1)/(3^n)$ is converges this is because common ratio in geometric series

here r is $(1)/(3)$ and here it satisfy that -1 < r < 1

so it is converges

and

$(sin(n))/(3^n)$ is also similar

so it is converges

and here no $(-1)^n$ term is

so we can say series is absolutely convergent

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Answers

Answer:

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Step-by-step explanation:

2x2+3xy+3xy
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Answers

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Answers

Answer: first one is 12 then second one is 10.5 then the third 9 then the fourth one is 7.5

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Which of the following values cannot be probabilities? 0.04, 5 divided by 3, 1, 0, 3 divided by 5, StartRoot 2 EndRoot, negative 0.59, 1.49 Select all the values that cannot be probabilities. A. 1.49 B. 1 C. three fifths D. StartRoot 2 EndRoot E. five thirds F. 0 G. negative 0.59 H. 0.04

Answers

Answer:

A. 1.49

D. √2

E. five thirds

G. - 0.59

Step-by-step explanation:

In order to be a probability, a value must be at least zero, or at most 1:

$0 \leq P\leq 1$

Evaluating each of the given values:

A. 1.49

1.49 is at least zero but it is greater than one, therefore 1.49 cannot be a probability.

B. 1

1 represents a probability of 100%, therefore this value can be a probability

C. three fifths

$0\leq (3)/(5) \leq 1$

Can be a probability

D. √2

$\sqrt 2 =1.41 > 1$

Cannot be a probability

E. five thirds

$(5)/(3)=1.67>1$

Cannot be a probability

F. 0

0 represents a probability of 0%, therefore this value can be a probability

G. - 0.59

Negative values cannot be probabilities.

H. 0.04

$0\leq 0.04 \leq 1$

Can be a probability

Final answer:

Probabilities are values ranging from 0 to 1, inclusive. With this in mind, values 5/3, √2, -0.59, and 1.49 cannot be probabilities as they're either below 0 or above 1.

Explanation:

In the field of mathematics, specifically in statistics, a probability represents the likelihood of an event occurring and is always a value between 0 and 1, inclusively. The value 0 means that an event will not happen, whilst 1 means the event is certain to happen. Therefore, any value less than 0 or greater than 1 cannot be a probability.

Given the values: 0.04, 5 divided by 3, 1, 0, 3 divided by 5, √2, negative 0.59, and 1.49, the values that cannot be probabilities are:

Value 5 divided by 3 (which equals approximately 1.67)
Value √2 (which equals approximately 1.41)
Negative 0.59
1.49

These numbers do not lie within the range of 0 to 1, and hence, cannot represent probabilities.

Learn more about Probability here:

brainly.com/question/22962752

#SP3

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