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
Pavel [41]
2 years ago
10

Does the following infinite series have a sum or not and does it converge or diverge?

Mathematics
1 answer:
iren [92.7K]2 years ago
3 0

Answer:

Step-by-step explanation:

Please present these numbers as a list:  7, -21, 63, -189, ....

Otherwise it appears that you are adding them up, which is not the case.

We can tell that this is a geometric series because each new number is -3 times the previous number:  -3(7) = -21, -3(-21) = 63, and so on.  Let r = -3 and a = first number = 7.

                                                                                                       a

The sum of an infinite geometric series exists if and only if |r} < 1.  Here, |-3|, or 3, so in this case the sum of the series does not exist.  That is, the series diverges.

You might be interested in
What is the amplitude of the cosine function corresponding to the secant function graphed below ? a. -2 b. -1 c. 2 d. 3
Bas_tet [7]

Answer:

2

Step-by-step explanation:

From the graph, we obtain the trigonometric function as:

y=2 \sec x+1

The corresponding cosine function have equation.

y=2\cos x+ 1

This function is of the form: y=a\cos bx+c

where |a| is the amplitude.

Therefore the amplitude is |2|=2

The third choice is correct

7 0
3 years ago
Graph the line with slope -3 passing through the point (2,4)
sveticcg [70]

Answer:

f(x) = -3x + 10

Step-by-step explanation:

Substitute values to find b;

y=mx+b

y=-3x+b

<em>Replace X and Y</em>

4=-3(2)+b

4=-6+b

<em>Swap sides to set equal to b. Swapping causes sign change</em>

4+6=b

10=b

4 0
2 years ago
Given the system of equations:
uranmaximum [27]

Answer:

x=4

y=2

Step-by-step explanation:

2x+2y=12

x−y=2

​In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

2x+2y=12,x−y=2

To make 2x and x equal, multiply all terms on each side of the first equation by 1 and all terms on each side of the second by 2.

2x+2y=12,2x+2(−1)y=2×2

Simplify.

2x+2y=12,2x−2y=4

Subtract 2x−2y=4 from 2x+2y=12 by subtracting like terms on each side of the equal sign.

2x−2x+2y+2y=12−4

Add 2x to −2x. Terms 2x and −2x cancel out, leaving an equation with only one variable that can be solved.

2y+2y=12−4

Add 2y to 2y.

4y=12−4

Add 12 to −4.

4y=8

Divide both sides by 4.

y=2

Substitute 2 for y in x−y=2. Because the resulting equation contains only one variable, you can solve for x directly.

x−2=2

Add 2 to both sides of the equation.

x=4

The system is now solved.

x=4,y=2

Correct choice is B) x=4.

8 0
2 years ago
Read 2 more answers
A square and a rectangle have equal area.The rectangle is 64 cm by 81 cm. What is the perimeter of the square?
Fittoniya [83]

Answer:

2592 cm

Step-by-step explanation:

square area = x²

rectangle area = bh

so

x² = bh

since the areas are equal

b and h are in the problem as 64 and 81

x² = 64x81

x² = 5184

divide by 2

x = 2592 cm

6 0
3 years ago
What is the formula for the pythagorem theory
Alex73 [517]

Answer:

C^2 = a^2 + b^2

The formula for the pythagorem theory

8 0
3 years ago
Read 2 more answers
Other questions:
  • 5 of 5
    13·1 answer
  • Factor the polynomial completely
    10·1 answer
  • In triangle ABC, A=32 degrees, a=8, and b=7. Find C
    14·1 answer
  • I need help “ write the following answer as a fraction :
    12·2 answers
  • -5/8x+2&gt;56/16 please help anything will do
    11·1 answer
  • Which trig ratio should you use to find the given side?
    14·1 answer
  • 6. Is it possible to have a regular polygon with<br>an exterior angle of measure 25°?​
    14·2 answers
  • Write the equation where m = 0 and passes through the point (-3, 1)
    10·1 answer
  • What are the advantages of using a table to find equivalent ratios?
    15·1 answer
  • The table shows how Mura spends her free time on a typical Saturday.if she has 6hours of free time how many hours does she spend
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!