Answer:
10 tapes and 6 Cds
Step-by-step explanation:
As tapes sell for $10 and CD sell for $15, let t be the number of tapes bought and c the number of cds, we can write an equation for the expenditure in the form:
10c + 16t = expenditure
We also n=know she spent 220, so:
10c + 16t = 220
As she bought 16 items, the sum of CD and tapes must be equal to 16. So:
c + t = 16
If we take this last equation and subtract t in both sides:
c = 16 - t
We got the number of CD depending on the number of tapes. We can replace this in the first equation to get t:
10 [16 - t] + 16t = 220
160 - 10 t +16t = 220
160 + 6t = 220
If we subtract 160 in both sides
6t = 220 - 160
6t = 60
Dividing both by 6:
t = 60/6 = 10
So, she purchased 10 tapes. As in total she purchased 16 items she must have purchased 6 cds.
Solution: She purchased 10 tapes and 6 CDs
Answer:
x will be -1
How it is written: x > -1
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 
.
F(1) = -f(0) +5 = -3 +5 = 2
f(2) = -f(1) +5 = -2 +5 = 3
f(2) = 3
_____
The sequence appears to alternate between 3 and 2.
