Answer: 
; 5
Step-by-step explanation:
Given series : ![[\dfrac{5}{1\cdot2}]+[\dfrac{5}{2\cdot3}]+[\dfrac{5}{3\cdot4}]+....+[\dfrac{5}{n\cdot(n+1)}]](https://tex.z-dn.net/?f=%5B%5Cdfrac%7B5%7D%7B1%5Ccdot2%7D%5D%2B%5B%5Cdfrac%7B5%7D%7B2%5Ccdot3%7D%5D%2B%5B%5Cdfrac%7B5%7D%7B3%5Ccdot4%7D%5D%2B....%2B%5B%5Cdfrac%7B5%7D%7Bn%5Ccdot%28n%2B1%29%7D%5D)
Sum of series = ![S_n=\sum^{\infty}_{1}\ [\dfrac{5}{n\cdot(n+1)}]=5[\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}]](https://tex.z-dn.net/?f=S_n%3D%5Csum%5E%7B%5Cinfty%7D_%7B1%7D%5C%20%5B%5Cdfrac%7B5%7D%7Bn%5Ccdot%28n%2B1%29%7D%5D%3D5%5B%5Csum%5E%7B%5Cinfty%7D_%7B1%7D%5Cdfrac%7B1%7D%7Bn%5Ccdot%28n%2B1%29%7D%5D)
Consider 
⇒ ![S_n=5\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}=5\sum^{\infty}_{1}[\dfrac{1}{n}-\dfrac{1}{n+1}]](https://tex.z-dn.net/?f=S_n%3D5%5Csum%5E%7B%5Cinfty%7D_%7B1%7D%5Cdfrac%7B1%7D%7Bn%5Ccdot%28n%2B1%29%7D%3D5%5Csum%5E%7B%5Cinfty%7D_%7B1%7D%5B%5Cdfrac%7B1%7D%7Bn%7D-%5Cdfrac%7B1%7D%7Bn%2B1%7D%5D)
Put values of n= 1,2,3,4,5,.....n
⇒ 
All terms get cancel but First and last terms left behind.
⇒
Formula for the nth partial sum of the series :
Also, 
Answer:
H. 13.5 in²
Step-by-step explanation:
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hope it helps...
have a great day!!
Assuming you meant to write: "xy + zy"
The answer is: xy + zy = y(x + z)
The one variable that appear multiple times is: "y". There are no coefficients (other than the implied coefficients of "1"; since "1" multiplied by any number equals that very number). Since "y" appears twice, we can "factor out" a "y" ; as follows:
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y(x+z).
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Take note of the distributive property of multiplication:
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a(b+c) = ab + ac ;
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AND: a(b-c) = ab - ac.
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Likewise: y(x+z) = yx +yz
= xy zy
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The frequency would be 60%.
You know how many times she rolled the dice (100) then it also tells you the dice rolled 6 40 times. So then we minus 100 by 4. Which will end up getting us 60. Which we can also write as 60%. So the frequency is 60%.
Answer: 
or 
Step-by-step explanation:
The volume of a cylinder can be found with the following formula:
Where "r" is the radius and "h" is the height of the cylinder.
In this case, let be:
- 
the volume of one of this cylinders and 
the volume of the other one.
- 
the radius of the first one and 
the radius of the other cylinder.
- 
the height of one of them and 
the height of the other cylinder.
Then:
Therefore, you know this:
Simplifying, you get:
Now, knowing the ratios given in the exercise, you can substitute them into the equation:
Evaluating, you get:
