For which positive integers k is the following series convergent? k > 1.The limit of the ratio will be 0 for k > 1, and the series converges for those values.
Determine for which positive integers k the following series is convergent, we need to analyze the series:
Σ [(n!)^2 / (kn)!], with n starting from 1 and going to infinity.
We will use the Ratio Test to check for convergence.
The Ratio Test states that if the limit as n approaches infinity of the absolute value of the ratio of consecutive terms (a_n+1 / a_n) is less than 1, the series converges.
First, we find the ratio of consecutive terms:
[(n+1)!]^2 / (k(n+1))! * (kn)! / [(n!)^2] = [(n+1)!]^2 * (kn)! / [(n!)^2 * (k(n+1))!]
Simplify the expression:
(n+1)^2 * (kn)! / [(n!)^2 * k * (kn + k)!]
Now, take the limit as n approaches infinity:
lim (n→∞) [(n+1)^2 * (kn)! / [(n!)^2 * k * (kn + k)!]]
As n approaches infinity, the denominator will grow faster than the numerator for k > 1. This is because the factorial function grows faster than a polynomial, and the extra k term in the denominator makes the denominator grow even faster for larger k values.
Therefore, the limit of the ratio will be 0 for k > 1, and the series converges for those values:
For which positive integers k is the following series convergent? k > 1.
Read more about positive integers.
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Help pls ^picture^
I really need this quick
Answer:
[tex]4.4*10^9[/tex]
Step-by-step explanation:
[tex]8.8(10^6)(5(10^2))\\=8800000*500\\=8.8*1000000*5*100\\=(8.8*5)*(1000000*100)\\=44*100000000\\=4400000000\\4400000000=4.4*10^9[/tex]
Please help due today
Our teacher hasn’t explained the concept yet but class was canceled today
Answer:
What grade is this?
Step-by-step explanation:
What are the 2 roots of the equation 2x^2-5x-3=0
Answer:
Hence, 3/2 and 1 are the roots of the equation.
Help ASAP I’ll give you brainlest
Answer:
5.33 OR 5 1/3
Step-by-step explanation:
3 x 2³ ÷ 2 x 4 -1 +2
3 x 8 ÷ 2 x 4 -1 + 2
24 ÷ 8 +1
24 ÷ 9
2.66 OR 2 2/3
Given: - 4x/7 > 10. Choose the solution set. {x | x < - } {x | x > - } {x | x > - } {x | x < - }
Answer:
{x | x < - 35 / 2}
Step-by-step explanation:
-4x / 7 > 10
Multiply both sides by 7
-4x /7 * 7 > 10 * 7
-4x > 70
Divide both sides by - 4
-4x / - 4 > 70 / - 4
x < - 35 / 2 (inequality sign changes)
Adrianna is two years older than Fernando, while Lucy is triple Fernando's age. If the sum of their ages is eighty-two, how old is Adrianna?
HELPPPP MEEEEE!!!!!!
Answer:
18
Step-by-step explanation:
x + (2+x)+ (3x) =82
x+x+3x= 82-2
5x=80
x= 16
Fernando is 16
Adrianna is 2 years older so she is 18
And Lucy is 3x 16=48
together 82
Select the correct answer.
What are the factors of the function represented by this graph?
A. (x − 4) and (x − 8)
B. (x − 4) and (x + 8)
C. (x + 4) and (x − 8)
D. (x + 4) and (x + 8)
The factors of the function represented by the graph are (x + 4) and (x - 8)
How to determine the factors of the function represented by the graph?From the question, we have the following parameters that can be used in our computation:
The graph
From the graph, we can see that:
The graph intersects with the x-axis at x = -4 and x = 8
So, we have
x = -4 and x = 8
Set the equations to 0
So, we have
x + 4 = 0 and x - 8 = 0
This means that the factors of the function represented by the graph are (x + 4) and (x - 8)
Read more about factors at
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HELPPPPP HELLPPPPPP Plsss
Answer:
1) -5
2) 21
3) 60
4) -52
5) -12
6) 31
7) -16
8) -27
9) 5
10) -11
11) 16
12) -24
13) 11
14) -36
15) 2
16) 36
17) -31
18) -48
19) -24
20) -21
The angle of depression from a window 10 m above the ground to a coin on the ground is
15°. Find the distance of the coin from the base of the building.
Answer:
37.3 m
Step-by-step explanation:
Let the distance of the coin to the base of the building be represented by x. Applying the required trigonometric function, we have:
Tan θ = [tex]\frac{Opposite}{Adjacent}[/tex]
Tan 15 = [tex]\frac{10}{x}[/tex]
0.2680 = [tex]\frac{10}{x}[/tex]
x = [tex]\frac{10}{0.2680}[/tex]
= 37.3134
x = 37.3 m
The distance of the coin from the base of the building is 37.3 m.
What is the meaning of a sample in mathematics?
Answer:
A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample.
Step-by-step explanation:
Is 7/5 greater than 11?
Answer:
no
Step-by-step explanation:
you take 7/5 and turn it into an improper fraction
you then have 1 2/5
1 2/5 is smaller then 11
Find the area of the triangle.
Probably of Carl solving the 10 problems if there's 20 to study and he knows 15 and ten of the 20 are on the test.
Answer:
1/3
Step-by-step explanation:
Probability of solving ten problems by Carl
Given
Total number of problems = 20
Number of problems studied by Carl = 15
Number of problems out of the 20 set of problem coming in test is 10
Case I - All ten problems come from the set of known 15 question
10/15 * 10/20 = 1/3
Andre says that 534+ 214= 712 because 748= 712. Identify his mistake.
Step-by-step explanation:
748 ≠ 712 so 534 + 214 only = 748 not 712
hi guys..............
please guys answer the correct answer
Answer:
12) 1.5(m - n)/b13) 2t/(2c + d)Step-by-step explanation:
Question 12)Slope between the points:
A(a + b, 4m - n) and B(a - b, m + 2n)Use slope formula:
Slope = (m + 2n - 4m + n)/(a - b - a - b) = (-3m + 3n)/(-2b) = (-3)(m - n)/(-2)b 1.5(m - n)/bQuestion 13)Slope between the points:
C(3c - d, s + t) and D(c - 2d, s - t)Use slope formula:
Slope = (s - t - s - t)/(c - 2d - 3c + d) = (-2t)/(-2c - d) = (-2)t/(-1)(2c + d) 2t/(2c + d)Solve for x : 80 + x = 100 - 14
Answer:
x=6
Step-by-step explanation:
100-14=86
86-80=6
Please help.
Algebra.
1. 5
2. 3
This is the answer
Answer:
question 1 should be 5 and question 2 should be 3
Step-by-step explanation:
The slope of a line passing through the point (5.-6) is 0.4.
Drag the proper numbers and signs to obtain the equation of the line in slope-intercept form.
Answer:
using formula y2-y1/x2-x1, x1= -6,x2= o, y1= 5,y2= 4
Step-by-step explanation:
4-5/0-(-6)
-1/0+6
-1/6
is your answer
Solve for value the two angles in the triangle and classify the triangle using the sides and angles
Step-by-step explanation:
x + 15 +2x + 66 = 180
3x + 81 = 180
3x = 99
x = 99/3 = 33
plz mark my answer as brainlist plzzzz.
hope this will be helpful to you.
Answer:
The angles are 66, 66, and 48 degrees
The triangle is isosceles because 2 angles are equal, thus two leg lengths are equal
Step-by-step explanation:
the sum of all three angles in a triangle = 180 degrees
66 + 2x + (x+15) = 180
simplify
66 +3x + 15 = 180
reduce
81 + 3x = 180
subtract 81 from each side
81 - 81 + 3x = 180 - 81
3x = 99
divide both sides by 3
3x/3 = 99/3
x = 33
need help in this show working please
Rafael and his sister bought snacks for movie night.
Rafael got 3 boxed candies and 1 bag of chips for $6.99.
His sister got 2 bags of chips and 1 boxed candy for $5.98.
Find the cost for 1 of each of these items in dollars.
Answer:
1. $2.33
2. $2.99
Step-by-step explanation:
$6.99/3
$5.98/2
Answer:
bag of chips is 2.19
boxed candy is 1.60
Step-by-step explanation:
Desmos Calcuator
The spinner below is divided into five equal-sized sectors. What is the probability that the spinner will stop on a number greater than 3?
Answer:
40%
Step-by-step explanation: If you have five equal-sized sectors, then the probability that the spinner will stop on 4 and 5 is 40%.
The probability that the spinner will stop on a number greater than 3 will be 0.4 or 40%.
What is probability?The probability of an event occurring is defined by probability.
Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
As per the given,
The spinner below is divided into five equal-sized sectors.
The probability of it stopping more than 3 = probability of stops at 4 + probability of stops at 5.
⇒ 1/5 + 1/5
⇒ 2/5 = 0.4
So, 0.4 x 100 = 40%
Hence "The probability that the spinner will stop on a number greater than 3 will be 0.4 or 40%".
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Help Please
Acellus:
Find the value of Y in angle measures and segment lengths
Answer:
4.3
Step-by-step explanation:
I hope this helps!
8(8p+8)=640 solve
Answer ASAP please
Answer:
p = 9
Step-by-step explanation:
8(8p + 8) = 640
use the dist property
64p + 64 = 640
-64 -64
64p = 576
divide by 64
p = 9
Answer:
9
Step-by-step explanation:
Which equation is the result of adding theses two equations -2x+4y=17 3x-10y=-3
Answer:
x=-79/4, y=-45/8. (-79/4, -45/8).
Step-by-step explanation:
-2x+4y=17
3x-10y=-3
---------------
3(-2x+4y)=3(17)
2(3x-10y)=2(-3)
----------------------
-6x+12y=51
6x-20y=-6
------------------
-8y=45
y=45/-8=-45/8
3x-10(-45/8)=-3
3x+450/8=-3
3x+225/4=-3
3x=-3-225/4
3x=-12/4-225/4
3x=-237/4
x=(-237/4)/3
x=(-237/4)(1/3)
x=-237/12=-79/4
Please answer the photo.
Answer:
the answer i think is C. AB
The cheerleading squad at Kensington High School had 18 members with the old coach. Now, with the new coach, there are 50% more members on the squad, how many members are on the squad now
Answer:
27 members
Step-by-step explanation:
So we have 18 members and we see a 50% increase in members.
So:
Now the squad is 150% of 18
We can set up a percent proportion
x/150=18/100
To solve, we do:
(150*18)/100 = x
27 = x
There is an easier way to do this with benchmark fractions.
We find 50% of 18 which is 9
And since it's a 50% increase, we add 9 to 18 and get 27
Let me know if you have any questions
Answer:
B) 8 + J
(It's saying my answer is too short, not too sure why)
En un hotel hay 67 habitaciones entre dobles y sencillas, si el número de camas es 92. ¿Cuántas habitaciones hay de cada tipo?
Answer:
25 dobles y 42 sencillas
Step-by-step explanation:
25 x 2 = 50 camas + 42 = 92
y 25 habitaciones dobles + 42 sencillas = 67
Due in 10 minutes please help !! ASAP Erin buys 2 packs of potatoes costing £2 each, 3 packs of carrots for £3 per pack, and 3 turnips costing 90p each.
If she pays with a £20 note, how much change would she get in pounds, £?
2(2) + 3(3) =
4 + 9 = 13
I don't know what 90p means but basically, u have to multiply that by 3 and add it to our current total which is 13.
Then, u substract the total cost from the 20 and you should get the change.