The nth term of a series is represented by an=2^n/5^n+1 ⋅n . George correctly applies the ratio test to determine whether the series converges or diverges. Which statement reflects George's conclusion? From the ratio test, r = 0.4. The series diverges.

From the ratio test, r = 0.4. The series converges.

From the ratio test, r = 4. The series converges.

From the ratio test, r = 4. The series diverges.

Answers

Answer 1

Answer:

Answer: From the ratio test, r = 0.4. The series converges.

The given term is: $a_(n)=(2^(n))/(5^(\left(n+1\right)))\cdot n$

So the next term is = $a_(n+1)=(2^(\left(n+1\right)))/(5^(\left(n+2\right)))\cdot\left(n+1\right)$

The ratio test is :

$lim_(n\to\infty)\left|(a_(n+1))/(a_(n))\right|=lim_(n\to\infty)\left|(2^(\left(n+1\right)))/(2^(n))\cdot(5^(\left(n+1\right)))/(5^(\left(n+2\right)))\cdot(\left(n+1\right))/(n)\right|$

$lim_(n\to\infty)\left|(a_(n+1))/(a_(n))\right|=lim_(n\to\infty)\left|2\cdot(1)/(5)\cdot(\left(n+1\right))/(n)\right|$

$lim_(n\to\infty)\left|(a_(n+1))/(a_(n))\right|=(2)/(5)lim_(n\to\infty)\left|1+(1)/(n)\right|$

$lim_(n\to\infty)\left|(a_(n+1))/(a_(n))\right|=(2)/(5)\left(1+0\right)$

$lim_(n\to\infty)\left|(a_(n+1))/(a_(n))\right|=0.4$

Since 0.4 < 1 so the series converges.

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Answer 2

Answer:

Answer: Choice B) r = 0.4; series converges

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Explanation:

Check out the attached image below to see the steps on how I computed r.

The value you should get is r = 0.4

Since r is less than 1, the series converges.

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Extra info:

If r > 1, then the series would diverge.

If r = 1, then the series may diverge, conditionally converge, or absolutely converge. Another test would be needed if you get r = 1.

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_
the answer is 83.3% because 5/6=0.83
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Answers

Answer:

144 π cubic meters

Step-by-step explanation:

Formula for surface area of sphere is :

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We know the volume V = 288*π cubic meters.

V = (4/3)*π*r^3

288*π = (4/3)π*r^3

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From the Great MysticChaCha :-) ...:-)

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Answers

The distance from the focus to the directrix is twice the focal length. Using the distance formula, 2.6+(-0.6) = 3.2. Half of this value is the focal length. 3.2/2 = 1.6. Therefore, the focal length of the parabola with a focus of (-3,2.6) and directrix of -0.6 is 1.6.

Final answer:

The focal length of a parabola is the distance from its focus to the directrix. In this case, the focal length is calculated to be 2.4 units.

Explanation:

In Mathematics, particularly in the study of conic sections, the focal length of a parabola is the distance from the focus to the directrix of the parabola. Given the focus as (-3, 2.6) and the directrix as (-0.6), we can calculate the focal length by using the formula for the distance between a point and a line in a plane, which is |x-x1|. |x-x1| is the absolute value of the difference between the x-coordinate of the focus and the equation of the directrix. Here, x1 is -3 (from the focus) and x is -0.6 (from the directrix). So, the focal length of the parabola is |-0.6 - (-3)| = |-0.6 + 3| = 2.4 units.

Learn more about Focal Length here:

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