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

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)

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!

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)

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:

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°.

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

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:

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

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"

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

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

Answers

Answer: -26

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

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

WILL GIVE BRAINLIEST

Answers

Answer:

Step-by-step explanation:

MN/sin72=10/sin18

MN=30.8

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

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:

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.

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

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

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

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

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

Answers

Answer:

6.25

Step-by-step explanation:

> 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]


[tex]18 \div 36[/tex]

Answers

Answer:

0.5

Step-by-step explanation:

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

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!

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

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!

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]

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:

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