The original series has terms (1 + 1/n + 4/n²) / (n² + 1) that are smaller than the terms of the convergent p-series (1/n²) for large n, by the Comparison Test, the original series also converges.
To determine whether the series converges or diverges, we can use the Comparison Test. The series in question is:
∑[(n² + n + 4) / (n⁴ + n²)], from n = 1 to infinity.
First, let's simplify the expression by dividing both the numerator and denominator by n²:
(n² + n + 4) / (n⁴ + n²) = (1 + 1/n + 4/n²) / (n² + 1).
Now, we'll compare this series with another series:
∑(1/n²), from n = 1 to infinity.
This is a p-series with p = 2, which is greater than 1, meaning it converges.
For more about converges:
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Answer the photo below thanks
Answer:
You're right, the answer is C.
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
I am not sure if it is B or C, but I can say that it is not A since the figure in A is rotated. Figure in B kinda looks like a reflection then C because if the figures were translated then the corner should be at one side. Sorry if that kinda confused you, but I added a picture of what I am trying to say for the figure in option B. I guess it is C.
Hope this helps, thank you !!
The number 6545 can be written as a product of a pair of positive two digit integers. What are these two integers?
Answer:
77 and 85
Step-by-step explanation:
Since the number 6545 ends in a 5, we can assume that one of the two digit numbers ends in a 5. I tried 55, 65, 75, and 85, and I just divided 6545 by those numbers until I got a two-digit positive integer as my answer,
85 * 77 = 6545
Therefore, the answer is 85 and 77.
I hope this helps!
A water rocket is launched froni a platform. The height,
h in metres, of the water rocket at time & seconds after
it is launched is h= -212 + 74 + 4. When does the water
rocket hit the ground?
Answer:
4.41seconds later
Step-by-step explanation:
Let the equation of the height reached by the water front be h = -2t^2+7t+4
The water hits the ground at h =0
Substitute
0 = -2t^2+7t+4
-2t^2+7t+4 = 0
2t^2 - 7t - 8 = 0
t = 7±√(-7)²-4(2)(-8)/2(2)
t = 7±√49+64/4
t = 7±√113/4
t = 7±10.63/4
t = 7+10.63/4
t = 17.3/4
t = 4.41s
Hence the water hit the ground 4.41seconda later
y=8x+b
8 x 2+76=92
What is the solution to the system of equations?
Answer:
31. 3-(4+7)/8 33. 2/(3+x)-x*y^2. 35. 3.1x^ 3-4x^(-2)-60/(x^2-1) 37. (2/3)/5. 39. ... 31. a. x(2 + 3x) b. x = 0, −2/3 33. a. ... No; the associated system of equations still.
9. Teresa was taking her two children to the zoo. She purchased 1 adult ticket for herself and 2 children's
tickets for a total of $18.20. A family of 5 was also visiting the zoo. -The family purchased 2 adult tickets and
3 children's tickets for a total of $30.90. How much money did an adult ticket cost?
Answer:
plz mark as brainliest
Step-by-step explanation:
$7.9
What is the radius and diameter of the following circle?
Answer:
radius=7.5, diameter=13
Step-by-step explanation:
diameter is the length across a circle through the middle, and it is given in the picture. radius is half of the diameter
The candy store has a stock of candy. They have 15 bags of tootsie rolls, 10 boxes of nerds, 12 bags of gummy
bears, 5 bags of M&M's and 22 bags of skittles. Find the ratio of nerds to skittles. Be sure to simplify.
Answer:
ratio of nerds to Skittles
= 10:22
= 5:11
CAN YALL HELP!!!!!!!!!!!!! 8TH GRADE
Answer:
C
The others are irrational numbers. C can be a rational number.
If you are making broccoli cheese soup the ratio of cheese to broccoli to broth is 5:6:10 if there is 100 parts broth how many of each ingredient should you use
Answer: See explanation
Step-by-step explanation:
Since there are 100 parts broth, the number to use for each ingredients will be:
Cheese = 5 × 100/10 = 5 × 10 = 50
Broccoli = 6 × 100/10 = 6 × 10 = 60
Broth = 100
Pls help me with this math problem
Answer:
12 ima shoot u
Step-by-step explanation:
finding value of x. PQR
P- 2x°
3
3
3
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Equilateral Triangles.
Since, we know that, all the sides of a triangle are equal, hence it is a Equilateral triangle.
Equilateral triangle has one all angles equal to 60°.
so, major angle P = 60°
hence, 2x=60°
===> x = 30°
2. it's not B
Write a rule for the linear function shown in the graph.
A. y = -5/2x - 1
B. y = 3x – 1
C. y = 2/5x + 1
D. y = 5/3x + 1
Answer:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
( 0 , 1 )
Equation Form:
x = 0 , y = 1
Step-by-step explanation:
Graph.
y = − 5/ 2 x − 1
y = 3 x − 1
y = 2/ 5 x + 1
y = 5/ 3 x + 1
11. If AB = BC and BC = CD, which property shows AB = CD?
Answer:
i belive its the transitive property
sry if im incorrect
A toy store had 789 games.
It sold 53 of these games.
How many games are at the store now?
I games
?
Answer:
736 games are at the store now
Step-by-step explanation:
789-53=736
Answer:
736
Step-by-step explanation:
789-53=736
1) Resolva as expressões numéricas. Não esqueça de deixar os cálculos.
a) 2 + 8-3-5 + 15 =
b) 12 + (35 - (10 + 2) +2] =
c) [(18+32) + 8 +5 3] + 6 =
d) 37 + (-25 - (-11 + 19 - 4)] =
e) 60 = {2 • (-7 + 18 = (-3 + 12)]} - [7 • (-3) - 18 = (-2) + 1) =
f) -8 +{-5 + [(8-12) + (13 + 12)] - 10) =
Answer:
a=17
b=37
c=117
d=8
e=
f=-2
Select the two points that the line would go through. Practice on a piece of paper in front of you.
(1,-3)
(4,1)
(6,3)
(2,-2)
Answer:
(1,-3), (2,-2)Step-by-step explanation:
The graph passes through (3, -1) and (0, -4)
The slope is:
(-4 - (-1))/-3 = -3/-3 = 1The y-intercept is given: -4
The line is:
y = x - 4See the graph
The points plotted as well and those on the line are:
(1,-3)(2,-2)The diagram at right shows a regular
hexagon
What is the area of the shaded region?
Round your answer to the nearest tenth.
I
20
20
Apothem Length: 10,3
Answer:
Nice
Step-by-step explanation:
PLEASE HELP!!! ILL GIVE BRAINLIEST, EXPLAIN YOUR ANSWER PLEASE
Answer: -20v^3 - 30x^2 +20
Step-by-step explanation:
simply multiply each term inside of the parentheses by -5.
Answer:
20v³ + 20 - 30x²
Step-by-step explanation:
multiply -5 by all three terms inside parentheses
(-5)(-4v³) + (-5)(-4) + (-5)(6x²)
20v³ + 20 - 30x²
If x= 1/3 is one of the solutions of an equation then what is the factor that gave us this solution
Answer:
3x - 1 = 0
Step-by-step explanation:
If x = 1/3
multiply both sides by 3
3 * x = 1/3 * 3
3x = 1
Subtract 1 from both sides ;
3x - 1 = 1 - 1
3x - 1 = 0 ( the factor which gives the solution)
3x - 1 = 0
3x = 1
Doavide both sides by 3
3x / 3 = 1/3
x = 1/ 3
cuántos encuentros son necesarios para una entrevista completa
HEY GUYS PLS HELP (kinda easy tho)
Answer:
74
Step-by-step explanation:
13 5-peso coins
9 1 peso coins
13 X 5 = 65
9 X 1 = 9
65+9 = 74
How do I do this??? Sorry for my sloppy hand writing I’m in a rush...and can someone pls tell me if I’m doing this right???
There are 4 identical wooden blocks that are 20 inches long, 2 inches wide, and 1 inch thick. If you glue them together, what is the difference of the largest and smallest outer surface area you can get?
Answer:
Step-by-step explanation:
5 inches wide, and 2 inches thick. if you glue them together(stacked) what is ... If you glue the largest area faces together you will get the smallest overall ... The total surface area of one of the blocks is 2 times 250 square inches plus 2 times ... 720 times 3 is 2160 minus 4 times 250 is 2160 minus 1000 is 1160.
the supplement of a 65° angle has a measure of
Answer:
115 degrees
Step-by-step explanation:
supplementary angles add up to 180 degrees, so if x is the angle you're trying to have you get:
[tex]x + 65 = 180\\x = 115[/tex]
Which is the simplified form of the expression below? 6w + 23 + 3w A. 3w+23 B. 6w+3w C. 6w+23 D. 9w+23
Answer:
D, 9w + 23
Step-by-step explanation:
Add like terms.
A local little league has a total of 60 players, of whom 40% are left-handed. How many left - handed players are there?
Answer:
24 players
Step-by-step explanation:
Answer:
24. 60 X 4/10 is 24
Step-by-step explanation:
NEED HELP ASAPPPPPP PLZZZZZ
Right one paragraph on
What is factoring by using GCF?
Answer:
GCF is the largest factor that all terms have in common.
Which values of a and b make the following equation true?
Answer:
a=11 , b=7
Step-by-step explanation:
When integer multiply with integer, the base were same, then we just add both powers.
for example
[tex]x {}^{2} \times {x}^{3} = {x}^{2 + 3} = {x}^{5} [/tex]
Given that ABCD is a parallelogram. Find the following
Answer:
m=8
m<A=83
m<D=97
Step-by-step explanation:
Angles that are opposite of each other in a parallelogram are equal. Knowing this, we can first conclude that angle A and angle C are equal. We can set up the following equation:
[tex]9m+11=8m+19[/tex]
Subtract both sides by 11
[tex]9m+11-11=8m+19-11\\9m=8m+8[/tex]
Subtract both sides by 8m
[tex]9m-8m=8m+8-8m\\m=8[/tex]
To calculate angle A, plug the value of m into its expression.
[tex]<A=9m+11\\<A=9(8)+11\\<A=72+11\\<A=83[/tex]
In a parallelogram, angles that share a side are supplementary, meaning they add up to 180 degrees. Therefore, angle A and angle D are supplementary. Knowing this, we can set up the following equation:
[tex]180=83+D[/tex]
Subtract both sides by 83
[tex]180-83=83+D-83\\97=D[/tex]
I hope this helps!
Please help!
If these two shapes are similar, what is the measure of missing length h?
Answer:
5
Step-by-step explanation: