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:
6x + 35
Step-by-step explanation:
First Distribute
8x + 3x + 15 -5x +20
Then collect like terms
6x + 35
to solve you would need the value of x to plug it!
Answer:
33 inches to the nearest inch.
Step-by-step explanation:
Length of an arc = rC where r = the radius and C is the angle through which it turns in radians.
So for the 23 inch radius: length = 23 * 135 * π / 180
and for the 9 inch radius: length = 9 * 135 * π / 180
The difference = 23 * 135 * π / 180 - 9 * 135 * π / 180
= 14 * 135 * π / 180
= 32.99 inches.