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Mama L [17]
3 years ago
11

Does this Series Converge or Diverge? What is the common ratio?

Mathematics
1 answer:
tatiyna3 years ago
3 0

Answer:

Converge

Step-by-step explanation:

Given geometric series

1,000+200+40+8+\dfrac{8}{5}+...

The first term of this geometric series is a_1=1,000.

Next terms can be obtained by dividing by 5 or multiplying by \frac{1}{5}:

a_2=1,000\cdot \dfrac{1}{5}=200\\ \\a_3=200\cdot \dfrac{1}{5}=40\\ \\a_4=40\cdot \dfrac{1}{5}=8\\ \\a_5=8\cdot \dfrac{1}{5}=\dfrac{8}{5}\\ \\...

The sum of this infinite geometric series is

S=\dfrac{a_1}{1-q}=\dfrac{1,000}{1-\frac{1}{5}}=\dfrac{1,000}{\frac{4}{5}}=1,250

Hence, this series is convergent

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Answer:

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Step-by-step explanation:

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3 years ago
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If u put 2500 in an account at an annual rate of 5.6 with interest compounded annually, what is annual percentage yield
Alexus [3.1K]

Answer:

5.6%

Step-by-step explanation:

The computation of the annual percentage yield is shown below:

Given that

Initial investment amount is 2,500

And, there is an annual rate of interest i.e. 5.6%

Since we have to determine the annual percentage yield i.e. equivalent to the annual rate of interest i.e. 5.6%

Hence, the above represent the answer

4 0
3 years ago
Find f. f ''(x) = −2 + 36x − 12x2, f(0) = 8, f '(0) = 18 f(x) =
Alik [6]
Integrate <span>f ''(x) = −2 + 36x − 12x2 with respect to x:

f '(x) = -2x + (36/2)x^2 - (12/3)x^3 + c.  Find c by letting x = 0 and using f(0)=8.

Then f '(0) = -2x + 18x^2 - 4x^3 + c = 18 (which was given).

Then             -0      + 0      - 0 + c = 18, so c = 18 and 

f '(x) = </span>-2x + 18x^2 - 4x^3 + 18.

Go through the same integration process to find f(x).
8 0
3 years ago
Slope and y intercept of y+10x=2
marissa [1.9K]
Slope is -10x
Y-intercept is 2
5 0
3 years ago
What equation has a slope of 2 and a y intercept of -5
DIA [1.3K]

Answer:

y=  2x - 5 equation has a slope of 2 and a y intercept of -5

Step-by-step explanation:

Given:

The slope  = 2

Intercept of y = -5

To Find:

The equation of the line = ?

Solution:

The slope-intercept form of a line is a way of writing the equation of a line so that the slope of the line and the y-intercept are easily identifiable. The slope is the steepness of the line, and the y-intercept is the place the line crosses the y-axis.

The equation of the line in the slope intercept form is

y = mx+b

where

m is the slope

b is the y intercept

Now substituting the given values we get

y  = (2)x  + (-5)

y=  2x - 5

8 0
3 years ago
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