Why does the common ratio in an infinite geometric series have to be between 1 and -1? Why doesn't -2 or 2 work? Please help with this. Thanks in advance!

Answers

Answer 1

Answer:

A n+1 / A n    the ratio of successive terms will be less than 1  if A is between -1 and 1    so successive terms will have a ratio less than 1 and can be determined

If A n+1 / A n > 1 then successive values of the given ratio will not approach a constant value

If you write the value of the nth term as L = a r^(n - 1) one can see that r^(n - 1)  approaches a fixed value if r between -1 and 1 but not if | r | > 1


Related Questions

Evaluate x(-1)(-7)
When x4

Answers

28

if X is equal to 4, 4 times -1 is -4 so we multiply -4 by -7 which equals 28 since a negative times a negative is a positive

calculate the median of 2,7,10,8,9,10,15



please do it step by step​

Answers

Answer: 9

Concept:

The median is the value separating the higher half of a data sample, a population, or a probability distribution, from the lower half.

In other words, the median of a set of data is the middlemost number or center value in the set.

Solve:

STEP ONE: Line up the terms in the set from least to most

Given = 2, 7, 10, 8, 9, 10, 15

Line up = 2, 7, 8, 9, 10, 10, 15

STEP TWO: Find the middlemost number

Given = 2, 7, 8, 9, 10, 10, 15

Since it is an odd set, therefore there should be the equal number of terms in the lower and higher half.

There are in total seven terms, therefore, the 4th term would be the middlemost, which is [tex]\boxed{9}[/tex].

Hope this helps!! :)

Please let me know if you have any questions

Jim and Em baked 33 macaroons.
Jim baked 5 more macaroons than Em. How manymacaroons did Jim bake?

Answers

Answer: 19 macaroons

Step-by-step explanation:

Let's create an equation to represent this situation. Let x represent the number of macaroons that Em made.

33=x+x+5

33=2x+5

33-5=2x+5-5

28=2x

28/2=2x/2

14=x

This means that Em made 14 macaroons.

14+5=19

Therefore, Jim baked 19 macaroons.

- 13 -2
2 - [ -1]³ + [ 1 6 ] - [ - 1 - [ - 3 ] |

Answers

23

Step-by-step explanation:

2 - [ -1]³ + [ 1 6 ] - [ - 1 - [ - 3 ]

= 2-[-1] + [16] -[-1]-[-3]

= 2+1+16+1+3

= 3+16+4

=3+20

= 23

0.8 divided 11.08 plz give me answer

Answers

Answer: 0.8/11.08= 0.07220216606 or .0.7

Hope this helps!

solve it fasrltttttt​

Answers

Answer:

answer::::: 9 . Is it true ?

What do you mean by the value of function?​

Answers

Answer:

The average value of the function over its domain

Please help me on 9 10 11 12

Answers

Answer:

9. 72

10. 67

11. 41

12. 67

What is the solution to the equation -2(2x + 4) + 10 = 8x + 14?

A.
x = 3.5

B.
x = -1

C.
x = 1

D.
x = -3.5

Answers

[tex]-2(2x+4)+10=8x+14\\\\-4x-8+10=8x+14\\\\-4x-8x=14+8-10\\\\-12x=12 \ \ /:(-12)\\\\\huge\boxed{x=-1}[/tex]

Answer:

-1

Step-by-step explanation:

-2(2x + 4) + 10 = 8x + 14

-4x - 8 + 10 = 8x + 14

-4x + 2 = 8x + 14

-4x - 8x = 14 - 2

-12x = 12

x = -12/12

x = -1

5. Is this function one-to-one? How do you know?
6. What is f(-1)?
7. What is f(2)?
8. What is f(0)?

Answers

Answer:

6. - f

7. 2 f

8. 0

Step-by-step explanation:

Too lazy to explain

someone helppp please show all your work ty!!

Answers

Step-by-step explanation:

3(x - 5) = 3x - 15

3x - 15 = 3x - 15

3x - 3x = -15 + 15

0 = 0

Hence,

Eric is correct because after solving we get the answer 0

Answer:

[tex]3(x - 5) = 3x - 15 \\ 3x - 15 = 3x - 15 \\ 0x = 0 \\ no \: solution \\ thank \: you[/tex]

Check all that apply
vertical angels must

A. be obtuse
B. be adjacent
C. have the same vertex
D. be congruent

Answers

Answer:

D. be congruent

Step-by-step explanation:

vertical angles are angles that are across from each other on intersecting lines and they are always congruent

Pierre travels by plane from Paris to Singapore. The plane leaves Paris at 16 35 on Thursday and arrives in Singapore 13 hours and 45 minutes later. The local time in Singapore is 6 hours ahead of the local time in Paris. Work out the day and time in Singapore when the plane arrives​

Answers

Step-by-step explanation:

16:35 plus 6 hours to account for them being 6 hours ahead is 22:35 off the bat. we then add 13.75 hours which goes to Friday at 12:20 pm.

Solve for inequality:
n/-4 >= 7

Answers

Answer:

n ≤ − 28

Step-by-step explanation:

Multiply to remove the fraction, then set equal to  

0  and solve.

Find the simple interest.
Principal
Rate
Time
$6000
20%
4 1/2 years

Answers

Answer:

$5,400. 20% of 6,000 = 1,200. 1,200 * 4 1/2 (4.5) = $5,400 (bonus: 6,000 + 5,400 = $11,400) hope this helps

Step-by-step explanation:

- Zombie

What rule must be applied when evaluating an expression in which the
operations have the same priority?

Answers

Answer:

see explanation

Step-by-step explanation:

When evaluating a expression in which operations have the same priority.

Then evaluate from left to right

Answer:

They are calculated from left to right.

Step-by-step explanation:

help plweaseeeee thanks ​

Answers

Answer:

first triangle (to left) b=8, second one c=17

Step-by-step explanation:

for the first triangle (one to the left) the hypotenuse is 9, so let's use the pythagorean formula.

A^2   +  B^2  = C^2

^              ^          ^

^              ^         Hypotenuse

^        second side

first side

Substitute:

5^2 + b^2 = 9^2

SImplify:

25+b^2 = 81

Reduce:

b^2 = 64

Simplify:

b=8

In the second triangle, we are given 2 sides.

Let's do the same thing we did in the first one.

Givens:

A = 8

B = 15

Find:

C

Substitute:

8^2 + 15^2 = c^2

Simplify

64 + 225 = c^2

Reduce:

289 = c^2

Let's now square root both sides

square root of 289 is 17

so we are left with this:

c=17

Phew, you did it!

Hope this helped :))

The set of ordered pairs (b,M)
where b is the number of bags of
mandarins on a shelf, and M is the
number of mandarins. Each bag
holds 12 mandarins, and the shelf
can hold at most 20 bags.

Answers

Domain and range are the possible values a function can take as input and output, respectively.

The domain of the relation is  [tex]0 \le b \le 20[/tex]The range of the relation is [tex]0 \le M \le 108[/tex]

Given that:

[tex](b,M) \to[/tex] The ordered pair

Where:

[tex]b \to[/tex] Number of bags of mandarins

[tex]M \to[/tex] Number of mandarins

To determine the domain and range, we consider the following:

b: represents the domainM: represents the range

The shelf can hold a maximum of 20 bags implies that the domain of the relation is from 0 to 20. i.e. [tex]0 \le b \le 20[/tex]

When there is no bag on the shelf, the number of mandarin is:

[tex]M = 12 \times 0 = 0[/tex]

When the shelf has the maximum (i.e. 20 bags), the number of mandarin is:

[tex]M = 12 \times 9 = 108[/tex]

This implies that the range of the relation is: [tex]0 \le M \le 108[/tex]

Read more about domain and range at: https://brainly.com/question/1632425

6m+n m=8 and n=7 evaluate please help please

Answers

Answer:

55

Step-by-step explanation:

m=8

then 6x8=48

n=7

then 1x7 is 7

48+7=55

Answer:

55

Step-by-step explanation:

6m+n

6(8)+7=?

48 + 7= 55

Always multiply and divide first. Then addition and subtraction.

hello, this is my last attempt to get it right so if you can please help me​

Answers

Answer:

138°

Step-by-step explanation:

x+115°=6x° [ being vertically opposite angle]

or, 115=6x - x

or, 115=5x

or, 115/5 =x

or, x=23

Then,

x+115°

= 23+115°

=138°

Mark me brainliest plz.

Hope it would be helpful for you

To which set of numbers does −38 belong?

integers
irrational numbers
natural numbers
whole numbers

Answers

Answer:

-38 is an integer

Step-by-step explanation:

An integer is a whole-valued positive or negative number or 0. They are generated from the set of counting numbers 1, 2, 3,… and the operation of subtraction. So -38 is an integer.

hope this this helps

:)

A boat can travel 333 miles on 37 gallons of gasoline. How much gasoline will it need to go 486 miles?

Answers

Answer:

TRFCCFEDF

Step-by-step explanation:

YHGR

Answer:  54 gallons

Work Shown:

(distance)/(gallons used) = (distance)/(gallons used)

(333 miles)/(37 gallons) = (486 miles)/(x gallons)

333/37 = 486/x

333x = 37*486 .... cross multiplication

333x = 17,982

x = (17,982)/333

x = 54 gallons

You need 54 gallons to travel 486 miles.

Solve the equation 3/4x=9

Answers

Answer:

3/4x = 9

4x = 3/9

4x = 1/3

x = 1/12

Answer:

x= 12

Step-by-step explanation:

[tex](\frac{4}{3})(\frac{3}{4}x)[/tex]= [tex]9\frac{4}{3}[/tex]

X= 12

Please mark me the Brainliest!

help with this question -8=-16+n​

Answers

Answer:

8

Step-by-step explanation:

-16-8=8

what is 640 divided by 20

Answers

Answer:

640/20 is 32

hope it's helpful

When the number 640 is divided by the number 20, the result is 32.

To divide 640 by 20, we perform long division or use the concept of division as the inverse of multiplication. By dividing 640 by 20, we are essentially finding how many times 20 can be evenly divided into 640.

On Dividing 640 by 20 yields a quotient of 32. This means that 20 can be divided into 640 exactly 32 times, without any remainder.

Thus, 640 divided by 20 is equal to 32. In simpler terms, if we distribute 640 items into 20 groups, each group will contain 32 items.

Learn more about Division here

https://brainly.com/question/2263644

#SPJ6

Find the number of terms in this polynomial.

–10t5 + 2t

Answers

Answer:

8t

Step-by-step explanation:

10t-2t= 8t

8t+5

PLEASE HELP ME!!!

In the diagram above, O is the centre of the circle with radius of 13 cm.
Given the chord KM = 24 cm, find the length of OP, in cm.​

Answers

Answer:

5

Step-by-step explanation:

Since Km is 24cm then MP = 12cm. We also know that OM = 13 is the radius.

So not OMP is a triple pythagoras with OP = 5 ( since 5, 12, 13 is a triple pythagoras)

Please help ill give you brainlest


Which statement is true when describing the absolute value of the point represented on the number line?

A) The absolute value of 7 is −7 because the number is seven units to the right of zero on the number line

B) The absolute value of 7 is positive 7 because the distance from zero to 7 on the number line is seven units.

C) The absolute value of 7 is −7 because zero is seven units to the left of 7 on the number line...

D) The absolute value of 7 is −3 because the number is 3 units to the left of 10 on the number line.


What is the absolute value of −9 on the number line?

A) 9

B) −9

C) 0

D) 1

Answers

the answer is 9!! hope this helps

The absolute value of 7 is positive 7 because the distance from zero to 7 on the number line is seven units.

The absolute value of -9 on the number line will be 9 units from zero.

Explanation:

The absolute value of a real number is only the number irrespective of its sign. For example: The absolute value of '6 is '6' and the absolute value of '-8 ' is 8.The absolute value of a number can also be thought of as the distance from zero along the number line of a real number.

Given :

1) Four statements describing absolute value.

2) The absolute value of -9 on a number line.

To find:

1) The true statement.

2) The absolute value of -9 on the number line.

Solution:

1)

The absolute value of a number can also be thought of as the distance from zero along the number line of a real number.

|7|=7

The absolute value of '7' is 7.

This is because the distance from zero to 7 on the number line is seven units.

The statement B is true.

2)

The absolute value of -9:

|-9|=9

The absolute value of -9 on the number line will be 9 units from zero.

(See the image attached)

Learn more about the absolute value here:

brainly.com/question/780403?referrer=searchResults

brainly.com/question/1301718?referrer=searchResults

Write f(x) = 2x2 – 44x + 185 in vertex form.



To write f(x) = 2x2 – 44x + 185, factor out
from the first two terms.

Next, form a perfect square trinomial keeping the value of the function equivalent:

f(x) = 2(x2 – 22x + 121) + 185 – 242

The function written in vertex form is f(x) =
(x –
)2 +
.

Answers

Answer:

Step-by-step explanation:

[tex]f(x)=2x^2-44x+185\\\\=2(x^2-2*11*x)+185\\\\=2(x^2-2*11*x+11^2)+185-2*121\\\\\boxed{f(x)=2(x-11)^2-57}\\\\vertex\ is\ (11,-57)[/tex]

Answer:

f(x) = 2(x - 11)² - 57

Step-by-step explanation:

Given

f(x) = 2x² - 44x + 185 ( factor out 2 from the first two terms )

f(x) = 2(x² - 22x) + 185

To complete the square

add/ subtract ( half the coefficient of the x- term )² to x² - 22x

f(x) = 2(x² + 2(- 11)x + 121 - 121 ) + 185

     = 2(x - 11)² + 2(- 121) + 185

    = 2(x - 11)² - 242 + 185

f(x) = 2(x - 11)² - 57 ← in vertex form

If a student didnt turn an assignment in on the 27th of august, and the teacher deducted 10 percent each day. How much credit would they get if they turned it in on the 1st of september?

Answers

Answer:

i have no idea

Step-by-step explanation:

Answer:

credit of 60= lost 40  points

Step-by-step explanation:

31-27= 4

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