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
kirill115 [55]
3 years ago
10

The sum of infinity of the series 2/3 – 4/3² + 2/3³ + 4/3⁴ is​

Mathematics
2 answers:
Levart [38]3 years ago
8 0

Answer:

  • 7/20

Step-by-step explanation:

<u>It seems there are two patterns in the series:</u>

  • 2/3, 2/3³, ... with a₁ = 2/3 and r = 1/9
  • - 4/3², 4/3⁴, ... with a₁ = -4/9 and r = -1/9

<u>Using sum of infinity of the geometric series formula:</u>

  • S∞ = a₁/(1 - r)

<u>Applying this to both patterns:</u>

  • S₁ = 2/3÷(1 - 1/9) = 2/3 ÷ 8/9 = 2/3×9/8 = 3/4
  • S₂ = -4/9÷(1 - (-1/9)) = -4/9÷10/9 = -4/9×9/10 = - 2/5

<u>Sum of the two results:</u>

  • 3/4 + (-2/5) =
  • 5/5*3/4 - 4/4*2/5 =
  • 15/20 - 8/20 =
  • 7/20
Brut [27]3 years ago
6 0

Answer:

\frac{3}{4}  -  \frac{2}{4}  =  \frac{1}{4}

You might be interested in
Find the perimeter and area
LekaFEV [45]

Answer:

Perimeter = 156

Area = 1029

Step-by-step explanation:

Perimeter = 65 +42 49

P = 156

Area = 49*42/2

A = 1029

3 0
4 years ago
Read 2 more answers
When making a long distance call from a certain pay phone, the first three minutes of a call cost $2.10. After that, each additi
Sauron [17]

Answer: the number of minutes of long distance call that one can make is lesser than or equal to 12 minutes.

Step-by-step explanation:

Let x represent the number of minutes of long distance call that one makes.

The first three minutes of a call cost $2.10. After that, each additional minute or portion of a minute of that call cost $0.45. This means that if x minutes of long distance call is made, the total cost would be

2.10 + 0.45(x - 3)

Therefore, the inequality to find the number of minutes one can call long distance for $6.15 is expressed as

2.10 + 0.45(x - 3) ≤ 6.15

2.10 + 0.45x - 1.35 ≤ 6.15

0.75 + 0.45x ≤ 6.15

0.45x ≤ 6.15 - 0.75

0.45x ≤ 5.4

x ≤ 5.4/0.45

x ≤ 12

4 0
4 years ago
Which statement is true?
valentinak56 [21]

Answer:

  |-3| = 3 and -|-4| = -4

Step-by-step explanation:

The absolute value function changes the sign to positive, if it isn't already. The usual rules of arithmetic and logic apply to these statements.

|-3| = 3 (true) and -|-4| = -4 (true)   ⇒ this statement is true

|-3| = 3 (true) and |-4| = -4 (false)   ⇒ this statement is false

-|3| = 3 (false) and |4| = 4 (true)   ⇒ this statement is false

|-3| = 3 (true) and -|4| = 4 (false)   ⇒ this statement is false

__

<em>Additional comment</em>

A compound "and" statement is only true if <u>all</u> of the parts of it are true.

8 0
2 years ago
WORTH 100 POINTS NEED DONE ASAP WRONG ANSWERS WILL BE REPORTED THANK YOUUU
zysi [14]

Answer:

3.

1.x=√(15²-12²)=√81=9

2.x=√(6²+6²)=6√2

3.c=√(√19²-√7²)=√(19-7)=√12

Step-by-step explanation:

4.h=10

a=b=x

we have

by using Pythagoras law

h²=x²+x²

100=2x²

x²=50

x=√50=5√2

both legs =5√2

7 0
3 years ago
4x+6&lt;-6<br> Solve for x put steps
chubhunter [2.5K]

First move the constant to the other side causing it to change sides

4x<-6-6

Then calculate the difference (-6-6)

4x<-12

Now divide both sides by 4

X<-3

Then you are left with your answer:

x<-3

Hope this helps! :3

4 0
4 years ago
Read 2 more answers
Other questions:
  • Which equation shows the quadratic formula used correctly to solve 7x^2=9+x for x?
    12·2 answers
  • WILL GIVE BRAINLIEST TO CORRECT ANSWER! HELP ASAP! I AM ON A TIME LIMIT! Classify the following triangle as acute, right or obtu
    10·2 answers
  • Can an obtuse triangle have a right angle? why or why not?
    6·1 answer
  • Y intercept of y=2x-3
    13·1 answer
  • I am really struggling with this question. please help.
    9·1 answer
  • The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $1 each and will sell 150
    12·1 answer
  • Which ordered pairs in the form (x, y) are solutions to the equation
    14·1 answer
  • Which measurement would Lan need to know when he buys flooring for his kitch
    5·1 answer
  • PLEASE HELP ME 16 POINTS PLEASE HELP
    12·2 answers
  • Could the triangle shown be a right angle YES or NO
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!