The sequence
diverges.
For given question,
We have been given a sequence 
We need to determine whether the sequence converges or diverges.
From given sequence we have, 
We use Ratio Test.
According to Ratio Test,
, where sequence converges if and only if |r| < 1.
Consider,
![\lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(n+1)^2}{(n+1)^3+5(n+1)}}{\frac{n^2}{n^3+5n}} |\\\\\\= \lim_{n \to \infty} |\frac{(n+1)^2(n^3+5n)}{n^2[(n+1)^3+5(n+1)]} |\\\\=\infty](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%7C%5Cfrac%7Ba_%7Bn%2B1%7D%7D%7Ba_n%7D%20%7C%5C%5C%5C%5C%3D%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%7C%5Cfrac%7B%5Cfrac%7B%28n%2B1%29%5E2%7D%7B%28n%2B1%29%5E3%2B5%28n%2B1%29%7D%7D%7B%5Cfrac%7Bn%5E2%7D%7Bn%5E3%2B5n%7D%7D%20%7C%5C%5C%5C%5C%5C%5C%3D%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%7C%5Cfrac%7B%28n%2B1%29%5E2%28n%5E3%2B5n%29%7D%7Bn%5E2%5B%28n%2B1%29%5E3%2B5%28n%2B1%29%5D%7D%20%7C%5C%5C%5C%5C%3D%5Cinfty)
Since
is not defined, the sequence
diverges.
Therefore, the sequence
diverges.
Learn more about the sequence here:
brainly.com/question/17175513
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Answer:
A is the answer
Step-by-step explanation:
According to BODMAS (or DMAS), first we add and then subtract
if both operations are of add, we add it at the same time
Use a calculator it will help.
We are asked to solve for the width "x" in the given problem. To visualize the problem, see attached drawing.
We have the area of the swimming pool such as:
Area SP = l x w
Area SP = 10 * 16
Area SP = 160 feet2
Area of the swimming pool plus the sidewalk with uniform width:
Area SP + SW = (10 + x) * (16 + x)
160 + 155 = 160 + 10x + 16x + x2
160 -160 + 155 = 26x + x2
155 = 26 x + x2
x2 + 26x -155= 0
Solving for x, we need to use quadratic formula and the answer is 5 feet.
The value of x is
<span>
5 feet. </span>