Using limits, it is found that the infinite sequence converges, as the limit does not go to infinity.
<h3>How do we verify if a sequence converges of diverges?</h3>
Suppose an infinity sequence defined by:
![\sum_{k = 0}^{\infty} f(k)](https://tex.z-dn.net/?f=%5Csum_%7Bk%20%3D%200%7D%5E%7B%5Cinfty%7D%20f%28k%29)
Then we have to calculate the following limit:
![\lim_{k \rightarrow \infty} f(k)](https://tex.z-dn.net/?f=%5Clim_%7Bk%20%5Crightarrow%20%5Cinfty%7D%20f%28k%29)
If the <u>limit goes to infinity</u>, the sequence diverges, otherwise it converges.
In this problem, the function that defines the sequence is:
![f(k) = \frac{k^3}{k^4 + 10}](https://tex.z-dn.net/?f=f%28k%29%20%3D%20%5Cfrac%7Bk%5E3%7D%7Bk%5E4%20%2B%2010%7D)
Hence the limit is:
![\lim_{k \rightarrow \infty} f(k) = \lim_{k \rightarrow \infty} \frac{k^3}{k^4 + 10} = \lim_{k \rightarrow \infty} \frac{k^3}{k^4} = \lim_{k \rightarrow \infty} \frac{1}{k} = \frac{1}{\infty} = 0](https://tex.z-dn.net/?f=%5Clim_%7Bk%20%5Crightarrow%20%5Cinfty%7D%20f%28k%29%20%3D%20%5Clim_%7Bk%20%5Crightarrow%20%5Cinfty%7D%20%5Cfrac%7Bk%5E3%7D%7Bk%5E4%20%2B%2010%7D%20%3D%20%5Clim_%7Bk%20%5Crightarrow%20%5Cinfty%7D%20%5Cfrac%7Bk%5E3%7D%7Bk%5E4%7D%20%3D%20%5Clim_%7Bk%20%5Crightarrow%20%5Cinfty%7D%20%5Cfrac%7B1%7D%7Bk%7D%20%3D%20%5Cfrac%7B1%7D%7B%5Cinfty%7D%20%3D%200)
Hence, the infinite sequence converges, as the limit does not go to infinity.
More can be learned about convergent sequences at brainly.com/question/6635869
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I dont kwon the answer to your question
Answer:
Yes, she can drew a right triangle with these sides
Step-by-step explanation:
To answer this question we first have to prove the Pythagorean theorem
h = hyoptenuse
a = leg 1
b = leg2
h² = a² + b²
We have to replace the values that they gave us in this formula
The hypotenuse always has to be the longest side of a right triangle
(14cm)² = (11.2cm)² + (8.4cm)²
196cm² = 125.44cm² + 70.56cm²
196cm² = 196cm²
As we can see, equality is fulfilled, so she is correct
Answer:
Option (2) and Option (4)
Step-by-step explanation:
From the picture attached,
Length of ladder AC = 20 feet
Height of the highest point of the ladder from ground AB = 16 ft
By Pythagoras theorem,
AC² = BC² + AB²
BC² = AC² - AB²
BC = ![\sqrt{(20)^2-(16)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%2820%29%5E2-%2816%29%5E2%7D)
= ![\sqrt{400-256}](https://tex.z-dn.net/?f=%5Csqrt%7B400-256%7D)
= ![\sqrt{144}](https://tex.z-dn.net/?f=%5Csqrt%7B144%7D)
= 12
Now, Sinθ = ![\frac{\text{Opposite side}}{\text{Hypotenuse}}=\frac{\text{AB}}{\text{AC}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BOpposite%20side%7D%7D%7B%5Ctext%7BHypotenuse%7D%7D%3D%5Cfrac%7B%5Ctext%7BAB%7D%7D%7B%5Ctext%7BAC%7D%7D)
= ![\frac{16}{20}](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B20%7D)
Cosθ = ![\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{\text{BC}}{\text{AC}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BAdjacent%20side%7D%7D%7B%5Ctext%7BHypotenuse%7D%7D%3D%5Cfrac%7B%5Ctext%7BBC%7D%7D%7B%5Ctext%7BAC%7D%7D)
= ![\frac{12}{20}](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B20%7D)
tanθ = ![\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{\text{AB}}{\text{BC}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BOpposite%20side%7D%7D%7B%5Ctext%7BAdjacent%20side%7D%7D%3D%5Cfrac%7B%5Ctext%7BAB%7D%7D%7B%5Ctext%7BBC%7D%7D)
= ![\frac{16}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B12%7D)
Therefore, Option (2) and Option (4) are the correct options.
Answer:
I would say 21.5 but if I'm wrong don't be mad I'm legit trash at math