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
Anika [276]
3 years ago
8

What is the sum of the geometric series

Mathematics
1 answer:
Sergio039 [100]3 years ago
5 0
Answer: 2343 / 256

Explanation

I will do this for you in two forms: 1) adding each term, and 2) using the general formula for the sum of geometric series.

1) Adding the terms:

 4
∑ 3 (3/4)^i = 3 (3/4)^0 + 3 (3/4)^1 + 3 (3/4)^2 + 3 (3/4)^3 + 3 (3/4)^4
i=0

= 3 + 9/4 + 27/16 + 81/64 + 243/256 = [256*3 + 27*16 + 64*9 + 4*81 + 243] / 256 =

= 2343 / 256

2) Using the formula:

n-1
∑ A (r^i) = A [1 - r^(n) ] / [ 1 - r]
i=0

Here n - 1 = 4 => n = 5

r = 3/4

A = 3

Therefore the sum is 3 [ 1 - (3/4)^5 ] / [ 1 - (3/4) ] =

= 3 [ 1 - (3^5) / (4^5) ] / [ 1/4 ] = 3 { [ (4^5) - (3^5) ] / (4^5) } / {1/4} =

= (3 * 781) / (4^5) / (1/4) =  3 * 781 / (4^4) = 2343 / 256

So, no doubt, the answer is 2343 / 256
You might be interested in
Are z³ and 3z equivelent?explain​
salantis [7]
Yes because you are multiplying 3 z’s and also 3z’s
7 0
4 years ago
(10+ 2)12-06)<br> What is the answer?
Nutka1998 [239]
10+2=12-06/6=6
Hope this helped you ^^
8 0
3 years ago
In a game for three students, one opens a book and multiplies the numbers of the facing pages. This student states the product,
Simora [160]
The facing page numbers are 134 and 135
7 0
3 years ago
Read 2 more answers
Simplify (6 +i)(8 – 3i)<br><br> 51 – 10i<br> 48 – 32i<br> 45 – 10i<br> 48 – 10i – 3i^2 ...?
mote1985 [20]
<span>= 48 - 18i + 8i - 3i</span>²<span>
= 48 – 10i – 3i</span>²
4 0
3 years ago
suppose six of these people are men, and the other six are women. in how many ways can they join hands for a circle dance, assum
Drupady [299]

Twelve people join hands for a circle dance.In how many ways can they do this? Suppose six of these people are men, and the other six are women. In how many ways can they join hands for a circle dance, assuming they alternate in gender around the circle

Answer:

86400 ways

Step-by-step explanation:

Since the circle can be rotated, the number of ways to arrange a distinct number of n objects in a circle will be (n−1)!.

Now, if we rotate the circle with the six women, we will see that there are 5! ways with which they can be placed in the circle.

After picking the places for the women, we will now fill each gap between two women with a man.

We have 6 men. Thus, number of ways to arrange the men is 6!

Thus,number of ways they can join hands for a circle dance, assuming they alternate in gender around the circle = 5! × 6! = 86400 ways

8 0
3 years ago
Other questions:
  • These types of lines have a zero slope
    8·1 answer
  • Crystal owes $8,950 on her Electronics Boutique credit card with a 18.4% interest rate. She owes $6,390 on her Miscellaneous Goo
    5·1 answer
  • What is the value of 5 in 756? write and draw to explain how you know
    11·2 answers
  • Which equation represents the graph of the linear function?
    12·1 answer
  • What is 2y/3+27+3y/4=-24
    7·1 answer
  • A survey was conducted of 450 high school students asking which class they prefer, math or
    7·2 answers
  • Given STU and DEF , what is m∠E
    9·1 answer
  • A few questions here sryy
    11·1 answer
  • 6(x-2)=-18 solve the equation
    14·2 answers
  • Simplify:<br> (12+14) x 8+ (8² +4²) =
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!