Answer:
Yes
Step-by-step explanation:
if it's a less than or equal to it goes from the left to the right and has a full dot
Answer:
D. - 2
Step-by-step explanation:
- 8 - (-6)
= - 8 + 6
= - 2
Answer:
Dilations which reduce or enlarge an object. Translations which move the object from one part on the graph to another. I have also learned about how to construct a perpendicular bisector.
Step-by-step explanation:
Answer:
Y is 150° and x is 30°
Step-by-step explanation:
i think its because the bottom angle near to 150° is a vertically opposite angle so yeah
Im not so sure myself
Answer:
Given series is divergent
Step-by-step explanation:
<u><em>Step(i):-</em></u>
By using Ratio test
![\lim_{n \to \infty} |\frac{a_{n+1} }{a_{n} } | = l](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%7C%5Cfrac%7Ba_%7Bn%2B1%7D%20%7D%7Ba_%7Bn%7D%20%7D%20%20%7C%20%3D%20l)
a)
'l' is finite then the given ∑aₙ is convergent
b)
Here 'l' is infinite then the ∑aₙ is divergent
<u><em>Step(ii):-</em></u>
Given aₙ = ![\frac{n!}{n}](https://tex.z-dn.net/?f=%5Cfrac%7Bn%21%7D%7Bn%7D)
![a_{n+1} = \frac{(n+1)!}{n+1}](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%20%3D%20%5Cfrac%7B%28n%2B1%29%21%7D%7Bn%2B1%7D)
![\lim_{n \to \infty} |\frac{a_{n+1} }{a_{n} } | = \lim_{n \to \infty} |\frac{\frac{(n+1)!}{n+1} }{\frac{n!}{n} } |](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%7C%5Cfrac%7Ba_%7Bn%2B1%7D%20%7D%7Ba_%7Bn%7D%20%7D%20%20%7C%20%3D%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%7C%5Cfrac%7B%5Cfrac%7B%28n%2B1%29%21%7D%7Bn%2B1%7D%20%7D%7B%5Cfrac%7Bn%21%7D%7Bn%7D%20%7D%20%7C)
we know that n ! = n (n-1) (n-2) ......3.2.1
and also (n+1) ! = (n+1)n!
![\lim_{n \to \infty} |\frac{a_{n+1} }{a_{n} } | = \lim_{n \to \infty} |\frac{\frac{n+1)n!}{n+1} }{\frac{n!}{n} } |](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%7C%5Cfrac%7Ba_%7Bn%2B1%7D%20%7D%7Ba_%7Bn%7D%20%7D%20%20%7C%20%3D%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%7C%5Cfrac%7B%5Cfrac%7Bn%2B1%29n%21%7D%7Bn%2B1%7D%20%7D%7B%5Cfrac%7Bn%21%7D%7Bn%7D%20%7D%20%7C)
![\lim_{n \to \infty} |\frac{a_{n+1} }{a_{n} } | = \lim_{n \to \infty} n](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%7C%5Cfrac%7Ba_%7Bn%2B1%7D%20%7D%7Ba_%7Bn%7D%20%7D%20%20%7C%20%3D%20%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20n)
= ∞
<em>Given sum of the series is divergent</em>