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Liono4ka [1.6K]
2 years ago
15

What are all values of x for which the series n 3^n/x^n converges

Mathematics
1 answer:
Eva8 [605]2 years ago
6 0

The interval of the convergence is x < -3 or x > 3 if the series n 3^n/x^n goes infinitely.

<h3>What is convergent of a series?</h3>

A series is convergent  if the series of its partial sums approaches a limit; that really is, when the values are added one after the other in the order defined by the numbers, the partial sums getting closer and closer to a certain number.

We can find the interval for the convergent by root test.

Like the Ratio Test, the root Test is used to determine absolute convergence (or not) with factorials, the ratio test is useful.

For the given series:

\sum^{\infty}_{n=0}\dfrac{3^n}{x^n}

As the series goes infinitely, we can use root test.

By the root test, the convergence interval will be;

The interval of convergence is:

x < -3 or x > 3   we can write this as:

|x| < 3

Thus, the interval of the convergence is x < -3 or x > 3 if the series n 3^n/x^n goes infinitely.

Learn more about the convergent of a series here:

brainly.com/question/15415793

#SPJ4

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Degger [83]

Answer:

y=-3x+10

Step-by-step explanation:

Since you know that the equation of the line is perpendicular to 1/3, you have to find the inverse of 1/3. You swap the denominator and numerator and make the number negative. In this case, it will be -3. Now that you know the slope is -3, you can use the equation y-y1=m(x-x1) where m is the slope. We know that the point (2,4) is in the graph so we can plug it into the equation. y-4=m(x-2). We know that the slope is -3 so we can plug it into the equation. y-4=-3(x-2). Simplify this to get y-4=-3x+6. Simplify this to get y=-3x+10. This means that the answer is y=-3x+10.

If this has helped you please mark as brainliest

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3 years ago
A park has 22 elm trees. Elm leaf beetles have been attacking the trees. After removing several of the diseased trees, there are
serg [7]

Answer: 9 elm trees were removed.

Step-by-step explanation:

Let x represent the number of elm trees removed.

The total number of elm trees in the park is 22. Elm leaf beetles have been attacking the trees. After removing several of the diseased trees, there are 13 healthy elm trees left. The equation to find the number of elm trees that were removed would be

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Subtracting 13 from the left hand side and the right hand side of the equation, it becomes

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3 years ago
Mari adds 4 spoons of honey to a pitcher of iced tea. Each spoonful holds 5 mL of honey How many mL of honey does Mari have in a
weeeeeb [17]

Alright, lets get started.

Mari adds 4 spoons of honey to a pitcher.

Each spoonful holds 5 mL of honey.

So, total ML of honey mari adds = 4 spoon * 5 ML = 20 ML

Answer : 20 mL of honey does Mari have in all.

Hope it will help :)

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