we have been asked to find the sum of the given geometric series
![\sum _{n=1}^4\left(\frac{1}{2}\right)^{n+1}](https://tex.z-dn.net/?f=%20%5Csum%20_%7Bn%3D1%7D%5E4%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E%7Bn%2B1%7D%20%20)
A geometric sequence has a constant ratio "r" and is given by
![r=\frac{a_{n+1}}{a_n}](https://tex.z-dn.net/?f=%20r%3D%5Cfrac%7Ba_%7Bn%2B1%7D%7D%7Ba_n%7D%20)
![a_n=\left(\frac{1}{2}\right)^{n+1},\:a_{n+1}=\left(\frac{1}{2}\right)^{\left(n+1\right)+1}](https://tex.z-dn.net/?f=%20a_n%3D%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E%7Bn%2B1%7D%2C%5C%3Aa_%7Bn%2B1%7D%3D%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E%7B%5Cleft%28n%2B1%5Cright%29%2B1%7D%20)
![r=\frac{\left(\frac{1}{2}\right)^{\left(n+1\right)+1}}{\left(\frac{1}{2}\right)^{n+1}}=\frac{1}{2}](https://tex.z-dn.net/?f=%20r%3D%5Cfrac%7B%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E%7B%5Cleft%28n%2B1%5Cright%29%2B1%7D%7D%7B%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E%7Bn%2B1%7D%7D%3D%5Cfrac%7B1%7D%7B2%7D%20)
The first term of the sequence is
![a_1=\left(\frac{1}{2}\right)^{1+1}=\frac{1}{4}](https://tex.z-dn.net/?f=%20a_1%3D%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E%7B1%2B1%7D%3D%5Cfrac%7B1%7D%7B4%7D%20)
Sum of the sequence is given by the formula
![S_n=a_1\frac{1-r^n}{1-r}](https://tex.z-dn.net/?f=%20S_n%3Da_1%5Cfrac%7B1-r%5En%7D%7B1-r%7D%20)
Plug in the values we get
![S_4=\frac{1}{4}\cdot \frac{1-\left(\frac{1}{2}\right)^4}{1-\frac{1}{2}}](https://tex.z-dn.net/?f=%20S_4%3D%5Cfrac%7B1%7D%7B4%7D%5Ccdot%20%5Cfrac%7B1-%5Cleft%28%5Cfrac%7B1%7D%7B2%7D%5Cright%29%5E4%7D%7B1-%5Cfrac%7B1%7D%7B2%7D%7D%20)
On simplification we get
![S_4=\frac{15}{32}](https://tex.z-dn.net/?f=%20S_4%3D%5Cfrac%7B15%7D%7B32%7D%20)
Hence sum![=\frac{15}{32}](https://tex.z-dn.net/?f=%20%3D%5Cfrac%7B15%7D%7B32%7D%20)
Answer:
5x-26
Step-by-step explanation:
3(3x-6)-4(x+2)
Distribute the 3 and -4.
9x-18-4x-8
Combine like terms.
5x-26
Answer:
1.8 km
Step-by-step explanation:
54 km/hr
54/60 = 0.9 km/min
In 2 mins:
0.9 × 2 = 1.8 km
SA=4pir^2
d/2=r
8/2=4
r=4
SA=4pi4^2
SA=4pi16
SA=64pi in^2
if want, aprox pi=3.14
SA=200.96 in^2
8 x 3 = 24
24 + 4 = 28
Now if 10 purses are made in 8 hours, and we can see we timesed 8, 3 times, thats 10 x 3 = 30
Now we take in to count the last 4 hours
30 + 4 = 34
And 4 is half of 8 so if we cut 10 in half we get 5.
So, the answer is 35
At least that's what I got :)