1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Artyom0805 [142]
3 years ago
7

Find the geometric sum: 40 + 20 + 10 + … + 0.078125

Mathematics
1 answer:
sveticcg [70]3 years ago
4 0
S=40+20+10+\cdots+0.078125
S=40\left(1+\dfrac12+\dfrac14+\cdots+\dfrac1{512}\right)
S=40\left(1+2^{-1}+2^{-2}+\cdots+2^{-9}\right)

2^{-1}S=40\left(2^{-1}+2^{-2}+2^{-3}+\cdots+2^{-10}\right)

\implies S-2^{-1}S=40\left(1-2^{-10}\right)
\implies\dfrac12S=40\left(1-\dfrac1{1024}\right)
\implies S=80\left(1-\dfrac1{1024}\right)=\dfrac{5115}{64}=79.921875
You might be interested in
Find the lenght of ab
DerKrebs [107]

Answer:

20.6 cm (im pretty sure lol)

Step-by-step explanation:

sine rule:

(ab = x)

13.5/sin41 = x/sin90

13.5sin90/sin41 = x

x = 20.57741667

ab = 20.6cm

7 0
3 years ago
Please help ASAP!<br><br> What is m∠CAD?<br> a.) 25º<br> b.) 90º<br> c.) 100º<br> d.) 115º
mars1129 [50]
<span>m∠CAD = 90 + 25 = 115
answer
</span><span>d.) 115º</span>
8 0
3 years ago
Read 2 more answers
Madison made her aunt a garden. The width is 6 5/6 ft and the length is 7 3/5 ft. What is the area of the garden and shown as a
Brums [2.3K]
Hello. How are you doing
5 0
2 years ago
Read 2 more answers
Kevin ran 5 miles in the race. How many yards did Kevin run? (1 mile = 1,760 yards) A. 10,560 yards B. 8,800 yards C. 1,755 yard
nexus9112 [7]
1,760 x 5 = 8,800
B. 8,800
6 0
3 years ago
PLS HELP ME ASAP WITH 1, 2, 5, 6, 11, and 12 PLS!!
melamori03 [73]
1-

number 2) is correct





2- 3) is true



11) Jacob is not correct. because 6radical 5 is irrational



12) radical 20 is an irrational number but

so a+b is irrational



but
\sqrt{225}  = 15 \\ it \: is \: rational

so b+c is rational



good luck
8 0
3 years ago
Other questions:
  • Add [1 -4 3 5]+[-2 6 -2 4]​
    5·2 answers
  • Drag each figure to show if it is similar to the figure shown or why it is not similar.
    8·1 answer
  • I REALLY NEED HELP NON THIS
    7·2 answers
  • Functions help?
    13·1 answer
  • On average people spend 1/4 of the time they sleep in a dream state. If Maxwell slept 10 hours last night, how much time did he
    14·2 answers
  • The vertex is where the line y=-2x+4 intersects with the axis of symmetry of x=7. How do you write a quadratic equation in verte
    11·1 answer
  • a car with a 20 gallon gas tank can go 25 miles on 1 gallon of gas. if the tank is full at the begining of the trip, how many ti
    6·1 answer
  • Y=kx and x is doubled what happens to y
    7·1 answer
  • Help asap??!!?!?!.....................................!
    6·1 answer
  • Which one would be the number line ???????
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!