find a formula for the nth partial sum of each series 4+(4/3)+(4/9) and use it to find the series’ sum of the series converges.

Answers

Answer 1

Answer:

We can see that:

a₀ = 4

a₁ = 4/3

a₂ = 4/9.

We easily can see that the n-th therm of this will be:

aₙ = 4/3^n.

Now, the denominator increases as n increases, then for a really large n, aₙ will tend asymptotically to zero. This means that this summation converges.

We can write this summation as:

4*∑(1/3)^n.

The sum for the first N-th therms is:

We know that for a summation:

1 + r + r^2 + r^3 + ... + r^N = (1 - r^(N + 1))/(1 - r)

4 + 4*(1/3) + 4*(1/3)^2 + ... + 4*(1/3)^N = 4*( 1 - (1/3)^(N + 1))/(1 - (1/3))

Now, for the complete sum we have that:

n = {0, 1, 2, ...}

We know that for a summation:

∑a*r^n

with n = {0, 1, ...}

the sum is = a/(1 + r).

in this case we have:

a = 4, r = 1/3.

Then the sum is:

S = 4/(1 - 1/3) = 4/(2/3) = 3*2 = 6


Related Questions

is 13.48 irrational or rational? ​

Answers

Answer:

It is irrational

Step-by-step explanation:

Rational numbers do not have decimals.

It’s rational and rational numbers can have decimals.

PLZZ ANSWER THE QUESTION ​

Answers

Answer:

c

Step-by-step explanation:

y = mx + b

”m” is the slope, so the slope is -2

”b” is the y - intercept, so the y - intercept is (0 , 1)

Harriet earns the same amount of money each day. Her gross pay at the end of 7 workdays is 35h+56 dollars. Which expression represents her gross pay each day?

5h+8
8h+5
7h+11.2
11.2h+7

Answers

Answer:

the answer is A.

Step-by-step explanation:

The 7 work days is represented by a linear equation

The expression that represents her gross pay each day is 5h + 8

What are linear equations?

Linear equations are equations that have constant rates

How to determine the linear equation

The earning at the end of 7 work days is represented as:

35h + 56

To calculate the gross pay, each day:

We divided the total earnings by 7

So, we have:

[tex]Gross =\frac{35h + 56}{7}[/tex]

Evaluate the quotient

[tex]Gross =5h + 8[/tex]

Hence, the expression that represents her gross pay each day is 5h + 8

Read more about linear equations at:

https://brainly.com/question/14323743

Convert 2∘F to ∘C round to one decimal place

Answers

Answer:

-16.7

Step-by-step explanation:

(2°F − 32) × 5/9 = -16.7°C

Find three consecutive even integers whose sum is -42

Answers

Answer:

Three consecutive even integers are x, x+2, x+4.

Step-by-step explanation:

Their sum is x+x+2+x+4 = 3x+6.

Hope this helped! <3

Write the slope-intercept form of the equation for
each graph described.
Line passing through (-2,-8) and (9,-8)

Answers

Answer:

y=-8

Step-by-step explanation:

First find the slope which is rise over run which equals (y2-y1)/(x2-x1)

(-8-(-8))/(9-(-2))

(-8+8)/(9+2)

0/11

slope = 0

Now you have the slope of 0. You can plug in one of the given point (x,y) to find b

-8=0(9)+b

-8=b

Combine everything

y=0x-8

y=-8

Face no more through a garden and travels 1 1/8 meters in 1 1/2 minutes what is the snail’s rate in minutes per meter? HELP ME I NEED IT ASAP

Answers

Answer:

4/3 per minute

Step-by-step explanation:

Samantha is training for a race. The distances of her training runs form an arithmetic sequence. She runs 1 mi the first day and 2 mi the seventh day.

a. What is the explicit definition for this sequence?



b. How far does she run on day 19?

Answers

B Because how far does she runs on day 19

which number line and equation show how to find the distance from -2 to 5?

Answers

Answer:B

Step-by-step explanation:

Answer: |2-5|

Step-by-step explanation:

That is the CORRECT answer. I swear ONG

74,626,831.08 ROUNDED TO THE TENTH.

Answers

Answer:

74,626,831.1

Step-by-step explanation:

You'd notice that in the 0.8 part that the number 8 is greater than 5, and with rounding, if the number if 5 or over, then you round the decimal place before it to a number higher.

emilio worked for 19.5 hours he earned 497.25 how much did he earn per hour?

Answers

Answer:

25.5 per hour

Step-by-step explanation:

497.25/19.5

Answer:

497.25 devided by 19.5= $25.5 per hour

Step-by-step explanation:

6x+2=3(3x+14)
set notation

Answers

Answer:

x= -40/3

Step-by-step explanation:

This is due soon today can somebody help?
35 points (if they're all right)​ comment if you don't know it

Answers

Answer:

1) P(1,0)Q(-2,3)R(-3,3)S(3,2)

2) (3,4)

3) (0,-4)

4) (1,2)

Step-by-step explanation:

Anyone willing to answer this?

Answers

Answer:

1. perpendicular; the opposite?

2. Parallel; the slopes are the same?

Step-by-step explanation:

Just use Math

way

Einstein's equation relating mass and
energy is given by the formula E = mc,
where m is the mass of an object and
<= 3 x 10 ms', the speed of light.
a Find how much energy is present in
a 1 kg mass. (1 kg ms-'= 1 joule)
(2 marks)

Answers

What is the question

HELP PLEASE PLEASE 50 PTS
The polynomial is missing the coefficient of the third and last terms.
729x3 – 1,458x2y + ____xy2 – ____y3
If the polynomial is factorable using the binomial theorem, what is the coefficient of xy2?
324
648
972
1,944

Answers

Answer:

C

Step-by-step explanation:

Ed2021

The missing coefficient of xy² is 972, option C is correct.

What is Polynomial?

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given polynomial is 729x³ – 1,458x²y + ____xy² – ____y³

To find the missing coefficients, we can use the fact that the polynomial is factorable using the binomial theorem.

According to the binomial theorem, the expansion of (a + b)^3 is:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Comparing this with the given polynomial, we can see that a = 9x and b = -2y.

Substituting these values in the binomial theorem, we get:

(9x - 2y)³ = (9x)³ + 3(9x)²(-2y) + 3(9x)(-2y)² + (-2y)³

Simplifying this expression, we get:

729x³ - 1,458x²y + 972xy² - 8y³

Therefore, the missing coefficient of xy² is 972, option C is correct.

To learn more on Polynomials click:

https://brainly.com/question/11536910

#SPJ3

Which equation represents a line which is parallel
to the line y
=
-2 +62

Answers

the answer is hard to find find a hint

Wayne created a dried fruit mix to use on his cereal this week. He
used 7 spoonfuls of raisins for every 3 spoonfuls of dried cherries.
If Wayne used 14 spoonfuls of raisins, how many spoonfuls of dried
cherries did he use?

Answers

Answer:

6

Step-by-step explanation:

i had this same problem :)

Pls help me I will pick brainliest

Answers

Answer:

What do you need help with?

Step-by-step explanation:

Answer:

??

Step-by-step explanation:

.

find the value of x.
The answer is 13, but I need to show my work

Thank you guys

Answers

Answer:

Know the properties of vertical angles.

Step-by-step explanation:

Vertical angles are equal to each other, so we must make them equal to each other in an equation:

6x+2=80

6x=78

x=13

does anyone know the answer to this question?

consider the sequence below. What are the next three terms in the sequence?
3, 7, 11, 15,....

Answers

It goes plus 4 every time, so the next three terms are 19, 23, and 27

Grace is measured for her annual check up. She is 28 1/5 inches tall. Last year she was 25 3/5 inches tall. How much did she grow in one year?

Answers

Answer:

2 3/5 inches in a year

Step-by-step explanation:

28 1/5 - 25 3/5 = 141/5 - 128/5 = 13/5 = 10/5 + 3/5 = 2 + 3/5 = 2 3/5


A scale drawing of a building needs to be made using the scale 1 in = 230 ft. How tall will the building in the scale drawing be if the building is 1380 ft tall?

Answers

1380/230 = 6 inches in the scale drawing

Which net represents this triangular prism?

Answers

Hanap ka nalang sa google vhie d ko den alam eh

Answer:

If you talking about iready. It's the first pink one.

Step-by-step explanation:

Simplify each of the following powers of i.
i^99

Answers

Answer:

i= sqrt (-1)

If the power is

- even then the value could be -1 or 1

-odd then the value could be -i or i

99 is odd so now is

-i if (99+1)/2 is even or is

i is (99+1)/2 is odd

Now check (99+1)/2= 100/2= 50,

50 is even so

i^99 = -i

Step-by-step explanation:

Give the person brainliest

g Statesville population in 2010 was about 24,700, and was growing by about 1% each year. If this continues, what will Statesville population be in 2018? [Round to the nearest person.]

Answers

Answer:

26,676population

Step-by-step explanation:

Population in 2010 = 24,700

If it grows yearly by 1%, increment per year is expressed as:

1% of 24,700

= 1/100×24700

= 247 populations

After 8years, population increase will be 247×8 = 1976 population

Statesville population in 2018 will be expressed as;

Population in 2010+increase after 8years

= 24700+1976

= 26,676 population

Hence statesville population in 2018 will be 26,676population

Help me plsss! I'll give u 10 points​

Answers

Answer:

1.02n

Step-by-step explanation:

We just have to simply the expression already given which will give you the equivalent expression.

n + 0.02n since these are like terms because of the variable "n", we can just add them together

n+0.02n

1.02n

1. Let f(x) be defined by the linear function graphed below and
g(x) = x2 - 9x + 14.
I
A. Describe the right end behavior of g(x).

Answers

Answer:

Step-by-step explanation:

A). g(x) = x² - 9x + 14

     Since coefficient of highest degree term (x²) is positive, parabola will open upwards.

    For any parabola opening upwards,

    Right end behavior,

    y → ∞ as x → ∞

B). Let the equation of the linear function is,

    f(x) = mx + b

    Where m = slope of the function

    b = y-intercept

    From the graph attached,

    Slope 'm' = [tex]\frac{\text{Rise}}{\text{Run}}=\frac{-(2+1)}{(0+1)}[/tex]

    m = -3

    b = -1

    Therefore, function 'f' will be,

    f(x) = (-3)x - 1

    f(x) = -3x - 1    

    g(x) = x² - 9x + 14

           = x² - 7x - 2x + 14

           = x(x - 7) - 2(x - 7)

           = (x - 2)(x - 7)

    If h(x) = f(x)g(x)

    h(x) = -(3x + 1)(x -2)(x - 7)

    For h(x) ≥ 0

    -(3x + 1)(x - 2)(x - 7) ≥ 0

     [tex]x\leq -\frac{1}{3}[/tex] Or 2 ≤ x ≤ 7

    Therefore, for 2 ≤ x ≤ 7, h(x) ≥ 0

C). If k(x) = [tex]\frac{h(x)}{(x-2)}[/tex]

    k(x) = [tex]\frac{-(3x+1)(x-2)(x-7)}{(x-2)}[/tex]

    k(x) = -(3x + 1)(x - 7)

    For k(x) = -56

    -(3x + 1)(x - 7) = -56

     3x² -20x - 7 = 56

     3x² - 20x - 63 = 0

     3x² - 27x + 7x - 63 = 0

     3x(x - 9) + 7(x - 9) = 0

     (3x + 7)(x - 9) = 0

     [tex]x=-\frac{7}{3},9[/tex]

Aging workers of the Neotropical termite, Neocapritermes taracua, develop blue crystal containing glands ("backpacks") on their backs, When they fight intruding termites and are hampered, these "blue" termites explode, and the glands spew a sticky liquid (Sobotnik et al. 2012). The following data are from an experiment that measured the toxicity of the blue substance. A single drop of the liquid extracted from blue termites was placed on individuals of a second termite species, Labiotermes labralis, and the number that were immobilized (dead or paralyzed) within 60 minutes was recorded. The frequency of this outcome was compared with a control treatment in which liquid from glands of "white" termites lacking the blue crystals was dropped instead.
Is the blue liquid toxic compared to liquid from white termites?
Liquid source Unharmed Immobilized
Blue workers 3 37
White workers 31 9

Answers

Answer:

The blue liquid is toxic

Step-by-step explanation:

From the calculations I have done and attached to this problem

Null hypothesis:

H0 : p1 <= p2

Alternate hypothesis:

H1 : p1 > p2

^p1 = 0.925

^p2 = 0.2250

^P = (x1 + x2)/(n1+n2)

= 0.575

After calculating, I got test statistics = 6.33 ( check attachment)

P(z > 6.33) = 0.0000

In conclusion, our pvalue has been found to be less than the level of significance 0.05 so we reject null hypothesis and accept that we have enough sample evidence that the blue liquid is more toxic in comparison to white one.

Please check attachment for calculated test statistics.

where does 17 lie between

Answers

Between 16 and 18. Hope this helps
Other Questions
The average of 4,-8,6,14,-3 is keep the sign of the number with the largest absolute value What major trends characterize U.S. employment patterns? Using lines of latitude, where are the temperate zones.Help!! what is y=3x^2+24x+45 Who served as President of the First Continental Congress? Benjamin RushThomas JeffersonJames MadisonJohn MarshallJohn JayJohn HancockJohn Dickinson x/7= -9need help with what is the x intercept for y= 3x - 8 What percent of 60 is 15? The density of a certain material is such that it weighs 5 kilograms for every 8.5 fluidounces of volume. Express this density in ounces per liter. Round your answer to thenearest whole number. Solve and show the steps to the picture attached What is the correct alignment during a solar eclipse? Explain the belief system of Deism. *HELP*. I need help on this stuff on I-ready... *HELP* Convert 6 feet to meters.Conversion table:1 meter = 3.281 feet WILL THANK, GIVE BRAINLEST, AND GIVE FIVE STARS TO FIRST AWANSER IF IT'S RIGHTq1:how many baby elephants were weighed q2:Which group weighed the most per item on the scale? How much did it weigh?q3:Which group weighed the least per item on the scale? How much did it weigh?You dont have to show your work Which sentence uses commas correctly?Jack's favorite breakfast is bacon and eggs, toast, and orange juice.Jack's favorite breakfast is bacon, and eggs, toast, and orange juice.Jack's favorite breakfast is bacon and eggs toast, and orange juice.Jack's favorite breakfast is bacon, and eggs, toast and orange juice. is the pronoun in parenthisis a subject or object pronoun (I) offered to buy supper for my best friend 10 pointsFind the DISTANCE between point (3, -8) and point (-11,5). * Which of the following statements is true?The number 0 is a natural number. The number is an integer. The value is a rational number. The number -5 is a real number.