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:
192 yd³
Step-by-step explanation:
The volume of a rectangular pyramid is given by the formula:
In this case: 
<h3>
It is equivalent to 2a+2b</h3>
We use the distributive property.
Multiply the outer term 2 by each term inside ('a' and b)
2 times a = 2a
2 times b = 2b
We add those results to get 2a+2b. We cannot combine these terms as they are not like terms.
Answer:
z=7
Step-by-step explanation:
3z+5=4z-2
5=4z-2-3z
5=z-2
5+2=z
7=z
z=7
Answer:
705,000
Step-by-step explanation:
To round to the nearest thousand, you look at the number to the right of 5. If the number is 5 or higher then you round 5 up. But it is 4 so you keep 5 the same. All of the numbers after 5 are now 0. 705,000
