For what values of x does the series ∑n=0[infinity]​n!(2x−3)n​ converge? (A) x=23​ only (B) 1

Answers

Answer 1

To satisfy the inequality, we need |2x - 3| = 0, the series ∑n=0[infinity]​n!(2x−3)n​ converges for x = 2/3.

To determine the values of x for which the series converges, we can use the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges.

Considering the given series, let's apply the ratio test:

lim(n→∞) |(n + 1)!(2x - 3)^(n + 1)| / (n!(2x - 3)^n)

= lim(n→∞) |(n + 1)(2x - 3)|

For the series to converge, this limit must be less than 1.

Simplifying the expression, we have |2x - 3| < 1/(n + 1).

As n approaches infinity, the right side of the inequality becomes arbitrarily small.

Thus, to satisfy the inequality, we need |2x - 3| = 0, which gives x = 2/3.

Therefore, the series converges for x = 2/3, which corresponds to option (A).

Learn more about consecutive terms here:  brainly.com/question/14171064

#SPJ11


Related Questions

> Find the area of a circle with diameter 12 yd. Use the value 3.14 and do not round your answer. Be sure to include the correct unit in your answer. 12 yd​

Answers

[tex]area = \pi {r}^{2} [/tex]

[tex]area = (3.14) {(6)}^{2} [/tex]

[tex]area = (3.14)(36)[/tex]

[tex]area = 113.04 \: yd[/tex]

AC =
Round your answer to the nearest hundredth.
?
с
A
20°
2
B
It’s 1.88

Answers

Answer:

AC=1.88

Step-by-step explanation:

cos 20 = AC/2

0.9397 = AC/2

AC = 1.88

the ratio of red marbles to blue marbles in a bag is 3:4. which of the following is a possible total number of marbles is it 21, 30, 32, or 40.​

Answers

Answer:

21

Step-by-step explanation:

so if the ratio is 3:4

then we can also write the ratio as 3x:4x

where the total is 7x marbles and we see we have to chose the one that is divisible by 7 which is 21.

if my answer helped please mark as brainliest.

Which ordered pair is on the graph of the function? O (-1,2) O (6,-3) O (-2,-4) O (-6, 4)​

Answers

Answer:

(6, -3)

Step-by-step explanation:

Given the similar polygons, what is the value of X?

Answers

Answer:

2

Step-by-step explanation:

Answer:

The answer is 20

Step-by-step explanation:

I did the homework and 20 was the correct answer

10squared correct to 6 decimal places ​

Answers

Answer:

3.162278

Step-by-step explanation:

√10= 3.16227766

then find the millionths place which is 3.16227766

then you round that number based on the number to the right of it which is a 6 so you round it up

so the answer is 3.162278

Please helpppp i just want to know if i sm doing it right

Answers

9514 1404 393

Answer:

  b)  -9.8t +18

Step-by-step explanation:

b) The instantaneous rate of change is the derivative of the height function. The power rule is separately applied to each term, and the results added.

  power rule: d/dx(x^n) = nx^(n-1)

Then the derivative is ...

  dh/dt = 2(-4.9t^1) +18(1 ·t^0)

  dh/dt = -9.8t +18

__

If you haven't been introduced to derivatives as such, then you find the instantaneous rate of change by finding the average rate of change over a vanishing interval.

  [tex]\dfrac{dh}{dt}=\displaystyle\lim\limits_{h\to 0}{ \dfrac{h(t+h)-h(t)}{h}}\\\\\dfrac{dh}{dt}=\lim\limits_{h\to 0}\dfrac{(-4.9(t+h)^2+18(t+h)+23)-(-4.9t^2+18t+23)}{h}\\\\\dfrac{dh}{dt}=\lim\limits_{h\to 0}\dfrac{-4.9(2th+h^2)+18h}{h}=\lim\limits_{h\to 0}{(-9.8t +18 -4.9h)}\\\\ \boxed{\dfrac{dh}{dt}=-9.8t +18}[/tex]

WILL GIVE BRAINLIEST

Answers

Answer:

Step-by-step explanation:

MN/sin72=10/sin18

MN=30.8

solve the system of linear equation by graphing​

Answers

Answer:

Step-by-step explanation:

x + 2 = -1/2x + 2

3/2x + 2 = 2

3/2x = 0

x = 0

y = 0 + 2

y = 2

(0, 2)

If AD=8 and BD=4, what is the length of DC⎯⎯⎯⎯⎯⎯?

The figure shows right triangle C A B with altitude A D to hypotenuse B C.

DC = 4
DC = 20
DC = 8
DC = 16

Answers

Answer:

the answer should be 16!

1 point
Which of the following lists is ordered correctly from greatest to least?

A. 1 lb, 2 lbs., 18 oz., 49oz.

B. 2 lbs., 49 oz., 18 oz., 1 lb.

C. 49 oz., 2 lbs., 18 oz., 1 lb.

D. 2 lbs., 49 oz., 1 lb., 18 oz.

Answers

Answer: C

Step-by-step explanation:

1 lb = 16 oz

2 lb = 32 oz

18 oz = 18 oz

49 oz = 49 oz

I am not a professional, I am simply using prior knowledge!

Note- It would mean the world to me if you could mark me brainliest!

Felix said quadrilateral ABCD is a parallelogram because
BE = DE. What was his error?

Answers

Answer:

There is no angle E in the quadilateral presented in the question. Also, the angles he used are not on opposite side.

Step-by-step explanation:

To classify a quadrilateral is a parallelogram, a quadrilateral with both pairs of opposite sides must be parallel or congruent, that is in a quadrilateral ABCD, angle AB must equal CD and angle AD must equal BC.

Hence, when Felix said quadrilateral ABCD is a parallelogram because of BE = DE. His error was that "there is no angle E in the quadrilateral presented in the question and the angle he used are not on opposite side"

En la tabla 1.8 se presentan los puntos de ebullición aproximados de algunos elementos de la tabla periodica flúor -180 hidrogeno -253 argón -186 helio -269 nitrógeno -196 neón -246 ¿Cuál es el elemento químico con el mayor punto de ebullición?¿ y con el menor?

Answers

Answer:

Lowest boiling point = helium.

Highest boiling point = fluorine

Step-by-step explanation:

Given :

fluorine -180

hydrogen -253

argon -186

helium -269

nitrogen -196

neon -246

Arranging the boxing points of each chemical element on a number line, the least which will be located to the leftmost part is Helium with a boiling point of - 269 ; while the highest will be fluorine which is - 186°C

plz solve it and help me for it​

Answers

Given:

Base angle of an isosceles triangle is 15 degrees more than its vertical angle.

To find:

The measure of each angle of the triangle.

Solution:

Let x be the vertical angle. Then,

One base angle = x+15 degrees

We know that base angles of an isosceles triangle are equal.

Another base angle = x+15 degrees

Now, the sum of all angles of a triangle is 180 degrees by the angle sum property.

[tex]x^\circ+(x+15)^\circ+(x+15)^\circ=180^\circ[/tex]          (Angle sum property)

[tex](3x+30)^\circ=180^\circ[/tex]

[tex]3x+30=180[/tex]

[tex]3x=180-30[/tex]

[tex]3x=150[/tex]

Divide both sides by 3.

[tex]x=\dfrac{150}{3}[/tex]

[tex]x=50[/tex]

The measure of base angles is

[tex](x+15)^\circ=(50+15)^\circ[/tex]

[tex](x+15)^\circ=65^\circ[/tex]

Therefore, the measure of angles are 50°, 65° and 65°.

The cost of 9 scarves is $56.25. What is the unit price?

Answers

Answer:

6.25

Step-by-step explanation:

Help please!!

Are these triangles similar

choices:

Both
Neither

Answers

Answer:

The blue triangle -- ∆QRS only

Step-by-step explanation:

They have the same angles (49° and 96°) and the third angle would be 35°. The pink triangle has none of the same angles measurements

you are looking toronto corto go to Macon and back (210 mites)
Come and go car Rentcs charges a base rate of $25 dollars and so 20 mit
Interstate cor Rental charges a base rate of $15 dollars and 5025 a miles
Cretestable, graon, and equchon for each plan.
Equation for Come and Go
Equatlon for Interstater
Come and Go
Interstate
150
210
240
270
which plan is the best plan for you. Justify your answer.
Ch) 2 + 2 x 25xb5

Answers

B would be ur answer :)) told

(-3, -14) and (0, -9)

Answers

Answer: -26

Step-by-step explanation: hope this helps :)

A country trying to decide whether to join the United Nations must determine whether it is willing to: O A. give up its own national laws in favor of international laws set by the UN. O B. occasionally go against its own interests in favor of international priorities. O C. supply a large number of military forces to the UN standing army. O D. leave any regional intergovernmental organizations it has already joined.​

Answers

Answer:

to guarantee equality for all

Step-by-step explanation:

The league of nations was created to prevent another global war

Whats 4x+2=2(x+6) ?
Just want to see your answers

Answers

Answer:

x = 5

Step-by-step explanation:

4x + 2 = 2(x + 6)

4x + 2 = 2x + 12 (after you distribute the 2)

add and subtract like terms

4x - 2x = 12 - 2

2x = 10

x = 5

you can double check by substituting the x with 5 in the equation

4 (5) + 2 = 2(5 + 6)

20 + 2 = 2(11)

22 = 22

pls pls help me! Trousers bought 1400 dollars with 20% discount. How much is the original price?​

Answers

Answer:1120 dollars. Δ

Step-by-step explanation:You will pay $1120 for a item with original price of $1400 when discounted 20%. In this example, if you buy an item at $1400 with 20% discount, you will pay 1400 - 280 = 1120 dollars.

#I hope this helps!!!

~Regards~

44014137


[tex]18 \div 36[/tex]

Answers

Answer:

0.5

Step-by-step explanation:

S
3 ft
Find the area of this figure.
Round your answer to the
nearest hundredth. Use
3.14 to approximate .
4 ft
5 ft
5 ft
A = [ ? ] ft2
Notice that only half of the circle is included in the figure!

Answers

9514 1404 393

Answer:

  26.13 ft²

Step-by-step explanation:

The total area is twice the area of the right triangles plus half the area of a circle of radius 3 ft.

  Semicircle area = (1/2)(πr²)

  semicircle area = (1/2)(3.14)(3 ft)² = 14.13 ft²

The area of the two right triangles is ...

  total triangular area = (3 ft)(4 ft) = 12 ft²

Then the area of the figure is ...

  figure area = semicircle area + total triangular area

  = 14.13 ft² + 12 ft² = 26.13 ft²

Answer: 26.13

Step-by-step explanation:

Which number is an irrational number?

1. 50

2. 36

3. 100

4. 81

Answers

Answer:

36

Step-by-step explanation:

Answer:

50 and that line thingy

Step-by-step explanation:

uh

help, please I don't understand ​

Answers

Answer:

The second top one. if they have ANY repeating y values its not a function

Step-by-step explanation:

Mark scored 138 points in 6 games. How many points did he score per game?

Answers

Answer:

23 Points

Explanation:  

The answer you are looking for is 23 points per game.

To find this answer, you simply divide 138 by 6.

I hope this helps!

Select whether each equation has no solution, one solution, or infinitely many solutions.( I need help)

Answers

Answer:

1. one solution

2. one solution

3. no solution

Step-by-step explanation:

1. x = 0

2. x = -¾

3. 0

Answer:

1.one solution

2.one solution

3. no solution

4. infinitly solution

Step-by-step explanation:

Complete this statement using >, <, or =

0.248_____0.259

Answers

Answer:

Here the most appropriate answer is '>'

Thus it will be 0.248 > 0.259

10 is 70% of what number? If necessary, round to the nearest tenth.

Answers

Answer:

The required answer is 7.

Step-by-step explanation:

=10*70/100

=7

0.7X = 10

10 / 0.7 = 14.23

Activity 3.
Convert the following to the indicated measurement:
1. 86 km
dam
9. 6, 600 min
hr
10. 415° F
2. 2 mi
in
3. 20 in
cm
11. 130 °C
-
F
4. 25.1 gal
الي
12. 2.3 gallon
qt
5. 45 acre
km
13. 632 ft
cord
6. 67.33 at
gal
14. 5.1 lb
grains
7. 90.67 km
ha
15. 1,800 oz
- kg
8. 6 days​

Answers

Activity 3.

Convert the following to the indicated measurement:

1. 86 km = 8600 dam

9. 6, 600 min = 110 htlrs

10. 415° F = 212.778° c

2. 2 mi = 126720 in

3. 20 in = 50.8 cm

11. 130 °C = 266° F

4. 25.1 gal = 100.4 qt

12. 2.3 gallon = 9.2 qt

5. 45 acre = 0.174 square km

13. 632 ft = 4.937 cords

6. 67.33 qt = 16.832 gallons

14. 5.1 lb = 35700 grains

7. 90.67 km = 9067 hectares

15. 1,800 oz = 51.029 kilograms

8. 6 days = 144 hours = 8640 minutes

(Please heart the answer if you find it helpful, it's a motivation for me to help more people)

Other Questions
Elevated levels of which of the following would increase the risk for atherosclerosis,which could eventually lead to heart attack or stroke?A. LDL cholesterolB. HDL cholesterolC. StatinsD. Insulin Divide the following polynomials. Then place the answer in the proper location on the grid. Write the quotient and remainder as a sum in this format: quotient, remainder/ divisor. Do not include parentheses in your answer. 8y square- 4y+1 over 2y-1 Data Blank______ is the collection of data from various sources for the purpose of data processing. Multiple choice question. summary management aggregation During early adolescence, girls' self-esteem tends to be lower and more vulnerable than boys' because as compared to boys, girls are more concerned about Help help pls, ASAP!!! (Geometry)Complete the proof A sauce should do all of the following except __________. What is the equation of the line that passes through the point (5,4) and has a slope of 2 Find the mean and standard deviation for the set of data. {22,21,20,4,19,6,24,11,26} A. mean: 17; standard deviation: 8.1 B. mean: 17; standard deviation: 7.53 C. mean: 20; standard deviation: 8.1 D. mean: 20; standard deviation: 7.53 What resum should be used in the following situation?Helga needs to get a job, but she doesn't have a lot of experience. She needs a resum that will highlight her skills and also have a brief work history included.curriculum vitaefunctionalchronologicalcombination What is the y-intercept of the function f(x)=-2/9x + 1/3? A college graduate expects to earn a salary of $55,000 during the first year after graduation and receive a 3% raise every year after that. What is the total income he will have received after ten years? 4. Kelly has a list of patient temperatures in Fahrenheit, but she needs them converted to Celsius. Help her convert thetemperatures using the formula(F-32) x = C. Note: temperatures are listed to the nearest tenth.MethodOralAxillaryRectalTemperature F98.2 F96.6 F100.1 FTemperature CCF why is decision necessary. If you borrow $800 for 10 years at an annual interest rate of 12%, how much will you pay altogether? Pleaseeee help asap!!!! Movie Critique:1. What is the context of the film? What historical period and what historical figures areincorporated into the film? Summarize the plot of the film.2. How accurate is the film? What parts of the film are historically accurate and what ismisrepresented? What lies, myths, misconceptions, or inaccuracies does the film present toaudiences? Lastly what truths are accurately described or could have gone into greater detail?3. How does the film expand your awareness of the past? What parts of the film are educationaland what parts are just entertainment? Did the film make an impact on you and did you find itengaging? The critique should be two to three pages and should be typewritten.Font Size ,12. Time New Roman. Double Spaced. 700-800 word count. Approximately ________ percent of federal judges have held some political office prior to their appointment to the supreme court. To determine whether the client is experiencing akathisia as an adverse effect of the medication haloperidol, what should the nurse observe the client for Which of the following is NOT a reason why parking lots can be more dangerous than the open road?The space is enclosedVehicles are traveling at high speedsBlind spots are everywherePedestrians can be walking anywhere Which is true regarding the Milgram obedience study How can a literary critic express the negative aspects of his or her review without being ill-tempered or putting the writer down?