We can use the fact that, for
,

Notice that
![\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{1-x}\right]=\dfrac1{(1-x)^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Cdfrac1%7B1-x%7D%5Cright%5D%3D%5Cdfrac1%7B%281-x%29%5E2%7D)
so that
![f(x)=\displaystyle\frac5{(1-x)^2}=5\frac{\mathrm d}{\mathrm dx}\left[\sum_{n=0}^\infty x^n\right]](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdisplaystyle%5Cfrac5%7B%281-x%29%5E2%7D%3D5%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20x%5En%5Cright%5D)



By the ratio test, this series converges if

so the series has radius of convergence
.
Answer:
f(- 3) = 18
Step-by-step explanation:
To evaluate f(- 3) substitute x = - 3 into f(x)
f(- 3) = (- 3)² - 2(- 3) + 3 = 9 + 6 + 3 = 18
Answer:
a) 
b) 
c) 
d) 
e) The intersection between the set A and B is the element c so then we have this:

Step-by-step explanation:
We have the following space provided:
![S= [a,b,c,d,e]](https://tex.z-dn.net/?f=%20S%3D%20%5Ba%2Cb%2Cc%2Cd%2Ce%5D)
With the following probabilities:

And we define the following events:
A= [a,b,c], B=[c,d,e]
For this case we can find the individual probabilities for A and B like this:


Determine:
a. P(A)

b. P(B)

c. P(A’)
From definition of complement we have this:

d. P(AUB)
Using the total law of probability we got:

For this case
, so if we replace we got:

e. P(AnB)
The intersection between the set A and B is the element c so then we have this:

Answer:14
Step-by-step explanation: