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WITCHER [35]
3 years ago
7

Which geometric series converges ???

Mathematics
2 answers:
ki77a [65]3 years ago
7 0

Answer:

C

Step-by-step explanation:

A geometric series will only converge if - 1 < r < 1

sum to infinity = \frac{a}{1-r}

The nth term formula for a geometric series is

a_{n} = ar^{n-1}

where a is the first term and r the common ratio

The only summation with - 1 < r < 1 is C where r = - 0.2

Savatey [412]3 years ago
7 0

Answer:  The correct option is

(C) \sum_{n=1}^{\infty}4(-0.2)^{n-1}.

Step-by-step explanation:  We are give to select the geometric series that converges.

We know that

the general (n-th) term of a common geometric series is given by

a_n=ar^{n-1}.

And the series converges if the modulus of the common ratio is less than 1, .e., |r| < 1.

Now, for the first infinite geometric series, we have

a_n=\dfrac{2}{3}(-3)^{n-1}.

So, the common ratio will be

r=-3~~~\Rightarrow |r|=3>1.

That is, the series will not converge. Option (A) is incorrect.

For the second geometric series, we have

a_n=5(-1)^{n-1}.

So, the common ratio will be

r=-1~~~\Rightarrow |r|=1.

That is, the series will not converge. Option (B) is incorrect.

For the third geometric series, we have

a_n=4(-0.2)^{n-1}.

So, the common ratio will be

r=-0.2~~~\Rightarrow |r|=0.2

That is, the series will CONVERGE. Option (C) is correct.

For the fourth geometric series, we have

a_n=0.6(-2)^{n-1}.

So, the common ratio will be

r=-2~~~\Rightarrow |r|=2>1.

That is, the series will not converge. Option (D) is incorrect.

Thus, (C) is the correct option.

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Answer:

The width  of the rectangle is 14'8",  and the length is 33'4"

Step-by-step explanation:

We're given two pieces of information:

The length is eight more than twice the width:

l = 2w + 4

The perimeter is 96 feet:

p = 96

We also need to apply one more piece of information that is not provided here, and that is the relationship between the perimeter of a rectangle, and it's length and width:

p = 2l + 2w

We can solve for w by plugging the other two values into the last:

p = 2w + 2l\\96 = 2w + 2(2w + 4)\\96 = 2w + 4w + 8\\88 = 6w\\3w = 44\\w = \frac{44}{3}\\w = 14\frac{2}{3}

Now we can find the length by plugging w into the first equation:

l = 2w + 4\\l = 2(14\frac{2}{3}) + 4\\l = 29\frac{1}{3} + 4\\l = 33\frac{1}{3}

One third of  a foot is four inches, so the width is 14'8" and the length is 33'4"

To make sure our answer is correct, we should plug those numbers back into the area equation and see if we're right:

p = 2l + 2w\\p = 2(33\frac{1}{3}) + 2(14\frac{2}{3})\\p = 66\frac{2}{3} + 29\frac{1}{3}\\p = 96

So we know our answer's correct

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Mrs. Mobley can jog 3 miles in 27 minutes. How many miles can she jog in 81 minutes?
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Answer:

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Step-by-step explanation:

You need to get 27 minutes to 81 minutes so you multiply 27 by 3, and that is 81, so you simply multiply 3 by 3 and get 9! Hope this helps! ;)

(27 x 3) = 81

(3 x3) = 9

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Answer:

Step-by-step explanation:

a(1) = -7 (given)

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a(4) = a(3) + 4 = 1 + 4 = 5

and so on.

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Answer:

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Next, after finding how much you have in total 96oz you then divide by how many people in this case is 8 then you get your answer.

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