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
Elis [28]
2 years ago
6

Which geometric series diverges? Three-fifths three-tenths three-twentieths StartFraction 3 Over 40 EndFraction ellipsis Negativ

e 10 4 minus eight-fifths StartFraction 16 Over 25 EndFraction minus ellipsis Sigma-Summation Underscript n = 1 Overscript infinity EndScripts two-thirds (negative 4) Superscript n minus 1 Sigma-Summation Underscript n = 1 Overscript infinity EndScripts (negative 12) (one-fifth) Superscript n minus 1.
Mathematics
1 answer:
Sholpan [36]2 years ago
7 0

The geometric series which diverges is shown in the option number c as the absolute value of the common ratio of this series 4.

\sum_{n=1 }^{\infty} \dfrac{2}{3}(-4)^{n-1}

<h3>What is geometric series diverges? </h3>

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

It can be given as,

a+ar+ ar^2+ ar^3+...

Here,

is the (<em>a</em>) first term of the sequence, and (<em>r</em>) is the common ratio.

To be a series as geometric series diverges, it should follow,

|r| > 1

First option given as,

3/5+3/10+3/20+3/40+ ...

Here, the common ratio is,

r=\dfrac{\dfrac{3}{10}}{\dfrac{3}{5}}\\r=\dfrac{1}{2}

The common ratio is less than one. Thus option a is not correct.

First option given as,

-10+4-8/4+18/25- ...

Here, the common ratio is,

r=\dfrac{4}{-10}\\r=\dfrac{-2}{5}

For the option number two the common ratio is (-2/5) which is less than 1. This option is also not correct.

In the option number c, the value of common ratio is -4. The absolute value of common ratio is,

|r|=|-4|\\|r|=4

The absolute value of this common ratio is more than one. Thus, this is the correct option.

The geometric series which diverges is shown in the option number c as the absolute value of the common ratio of this series 4.

\sum_{n=1 }^{\infty} \dfrac{2}{3}(-4)^{n-1}

Learn more about the geometric sequence here;

brainly.com/question/1509142

You might be interested in
It took team rise over run 1 2/3 hours to hike 4 2/3 miles. What is their average speed in miles per hour?
pogonyaev

To find their average miles per hour we can divide the total miles by the hour used:

4 2/3 ÷ 1 2/3

=4x3+2/3 ÷ 1x3+2/3

=14/3 ÷ 5/3

In division, when we switch the place of numerator and denominator, we can change it to multiplication which makes the calculation easier as we can factorize the numbers.

=14/3 x 3/5

Factorize 3 in both amounts:

=14/1 x 5/1

=14/5

=2.8 miles/hour

Therefore their average speed is 2.8 miles/hour.

Hope it helps!

8 0
2 years ago
Joan decided to look at new SUVs.Joan found a used SUV for$6000.Joan found that she paid 25% of the price of a new SUV . How muc
UNO [17]
A new SUV would cost $24,000 because 25% is 1/4 , so $6,000 times 4 =$24,000
3 0
3 years ago
Penny is counting the days until her grandma comes to visit. There are 98 days left. How many weeks are left until Penny's grand
Lorico [155]
Create a unit rate.
1 wk/ 7 days
x wk/ 98 days
Cross multiply.
98=7x
Solve the equation.
14=x
14 weeks until her grandmother visits
3 0
3 years ago
As part of a class project, a university student surveyed the students in the cafeteria lunch line to look for a relationship be
Vedmedyk [2.9K]

Answer:

0.63

Step-by-step explanation:

To get the relative frequency of students with red hair, we need to find the relative frequency of students with red hair from the students with gray eyes.

Since we already know that the total number of students with gray eyes is 35 and the number of red hair students with gray eye is 22

The formula we will use to calculate the relative frequency will be

The relative frequency of students with red hair = Total students of red hair with gray eyes divide by total number of gray eye students

22 ÷ 35 = 0.628  ≅ 0.63

6 1
3 years ago
Your school is choosing a new school mascot to represent all team sports. which group should you ask to get a random sample of s
ser-zykov [4K]
Answer: B. Every 10th students that enters the cafeteria

Explanation:

B is a random sample, while A, C, and D are biased.
5 0
3 years ago
Other questions:
  • Lesson 8 homework practice solve percent problems
    15·2 answers
  • The population in Rochester, New York, was 219,773 people in 2000 and 210,565 people in 2010. By about what percent did the popu
    10·1 answer
  • Rachel is collecting donations for the local animal shelter. So far she has collected $245, which is 70% of what she hopes to co
    14·1 answer
  • What are three consecutive integers whose product is 480 more than their sum?
    11·1 answer
  • What does -4(3x-4)=44<br> What is x
    7·1 answer
  • 14feet 23feet round each measurement to the nearest ten
    5·2 answers
  • Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
    12·2 answers
  • Help me plzzzzzzzzzzzzzz
    14·1 answer
  • Hey y’all. I’m so embarrassed and I want to hit my head so BAD:( I’m literally crying. So I had a test in math and I’ve always b
    10·2 answers
  • Evaluate functions : k(6) =
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!