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geniusboy [140]
1 year ago
12

Determine whether the series is convergent or divergent. if it is convergent, find its sum. (if the quantity diverges, enter div

erges.) 1 9 1 18 1 27 1 36 1 45
Mathematics
1 answer:
Lemur [1.5K]1 year ago
7 0

The geometric series is convergent and the value is 16.

<h3>How to illustrate the information?</h3>

Recall that the sum of an infinite geometric series, S, given first term, t_1, and common ratio, r, is given by:

S = t_1/(1 - r)

Note that:

3 = (4)(3/4)

9/4 = (3)(3/4)

27/16 = (9/4)(3/4)

So this a geometric series with t_1 = 4 and r = 3/4. Therefore:

4 + 3 + 9/4 + 27/16 + ... = 4/(1 - 3/4) = 4/(1/4) = 16

The correct option is 16.

Learn more about geometric series on:

brainly.com/question/24643676

#SPJ4

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum

4+3+ 9/4 +27/16 +???

choices are

1. 3/4

2. 12

3. 4

4. divergent

5. 16

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For this you simply need to give both fractions a common denominator!

The easiest way to do this specific problem would be to make the denominator 12. Why 12? Because 4 x 3 = 12.

So:

1/4 --> ?/12 --> 1 (3) / 12 --> 3/12

2/3 --> ?/12 --> 2 (4) / 12 --> 8/12

Total amount of time means the sum (adding them together).

When adding fractions, you MUST have a common denominator! (Which is what we just did).

So 3/12 + 8/12 = (8+3) / 12 = 11/12 hours

Notice how the denominator stayed the same? When adding/subtracting fractions, the denominator stays the same! :)

Hope this helped!

-------------------------------

DISCLAIMER: I am not a professional tutor or have any professional background in your subject. Please do not copy my work down, as that will only make things harder for you in the long run. Take the time to really understand this, and it'll make future problems easier. I am human, and may make mistakes, despite my best efforts. Again, I possess no professional background in your subject, so anything you do with my help will be your responsibility. Thank you for reading this, and have a wonderful day/night!
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What is the value of c such that the line y=2x+3 is tangent to the parabola y=cx^2
satela [25.4K]

The value of c such that the line y = 2\cdot x + 3 is tangent to the parabola y = c\cdot x^{2} is -\frac{1}{3}.

If y = 2\cdot x + 3 is a line <em>tangent</em> to the parabola y = c\cdot x^{2}, then we must observe the following condition, that is, the slope of the line is equal to the <em>first</em> derivative of the parabola:

2\cdot c \cdot x = 2 (1)

Then, we have the following system of equations:

y = 2\cdot x + 3 (1)

y = c\cdot x^{2} (2)

c\cdot x = 1 (3)

Whose solution is shown below:

By (3):

c =\frac{1}{x}

(3) in (2):

y = x (4)

(4) in (1):

y = -3

x = -3

c = -\frac{1}{3}

The value of c such that the line y = 2\cdot x + 3 is tangent to the parabola y = c\cdot x^{2} is -\frac{1}{3}.

We kindly invite to check this question on tangent lines: brainly.com/question/13424370

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