The given series is:
∑(n=1 to ∞) (8x^5)^n/n^2
We can use the ratio test to determine the radius of convergence:
lim (n→∞) |(8x^5)^(n+1)/(n+1)^2| / |(8x^5)^n/n^2|
= lim (n→∞) (8x^5)/(n+1)^2 * n^2/(8x^5)
= lim (n→∞) n^2/(n+1)^2
= 1
The radius of convergence is:
r = 1/8
To find the interval of convergence, we need to test the endpoints x = -r and x = r:
When x = -r = -1/8:
∑(n=1 to ∞) (8(-1/8)^5)^n/n^2 = ∑(n=1 to ∞) (-1)^n/n^2
This is an alternating series with decreasing terms, so we can use the alternating series test to show that it converges. Therefore, the series converges when x = -1/8.
When x = r = 1/8:
∑(n=1 to ∞) (8(1/8)^5)^n/n^2 = ∑(n=1 to ∞) 1/n^2
This is a convergent p-series with p = 2, so it converges by the p-series test. Therefore, the series converges when x = 1/8.
The interval of convergence is therefore:
i = [-1/8, 1/8]
To know more about radius of convergence , refer here :
https://brainly.com/question/28158009#
#SPJ11
need help please will mark you brainliests please give reason to
Answer:
angle BAD = 180 -2x
angle BCD = x given
angle BCD is an inscribed angle
angle DOB = 2 (angle BCD)
angle BAD = 180 -angle DOB 2 tangent theorem
Step-by-step explanation:
Answer:
[tex] m\angle BAD= (180 - 2x)\degree [/tex]
Step-by-step explanation:
[tex] m\widehat {BD} =2\times m\angle BCD[/tex]
(By inscribed angle theorem)
[tex] m\widehat {BD} =2x\degree [/tex]
[tex] m\widehat {BCD} =360\degree - m\widehat {BD}[/tex]
(By arc sum property of a circle)
[tex] m\widehat {BCD} =360\degree - 2x\degree [/tex]
[tex] m\angle BAD=\frac{1}{2} (m\widehat {BCD}-m\widehat {BD}) [/tex]
(by property of intersecting tangents outside of the circle)
[tex] m\angle BAD=\frac{1}{2} [(360\degree - 2x\degree) -2x\degree] [/tex]
[tex] m\angle BAD=\frac{1}{2} (360\degree - 2x\degree -2x\degree) [/tex]
[tex] m\angle BAD=\frac{1}{2} (360\degree - 4x\degree) [/tex]
[tex] m\angle BAD=\frac{1}{2} \times 2(180\degree - 2x\degree) [/tex]
[tex] m\angle BAD= (180 - 2x) \degree [/tex]
10(x-5)= -80
what is the value of the x
Answer:
x = -3
Step-by-step explanation:
10(x-5) = -80
10x - 50 = -80
10x -50 + 50 = -80 + 50
10x = -30
10x ÷ 10 = -30 ÷ 10
x = -3
Find the value x.
Need help....thank you
Step-by-step explanation:
It is parallel to the third side and has a length equal to half the length of the third side.
so
x= 34/2= 17
x= 17
Jasmine correctly answered 9 out of 10 of the game questions. What percent did she answer correctly.
Which correctly explains how to estimate 55 percent of 64?
Round 55 percent to 40 percent and 64 to 60. Think of 40 percer
Round 55 percent to 60 percent and 64 to 70. Think of 60 percent
Round 55 percent to 50 percent and 64 to 70. Think of 50 percent a
O Round 55 percent to 50 percent and 64 to 60. Think of 50 percent as
Answer:
i wanna say b
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
because i ate hamburger
Write an equation in standard form passing through the points (-2,0) and (-3,-1).
Tres hermanos van a repartirse un pastel y medio, cuanto le toco de pastel a cada uno de los hermnos
Answer:
medio pastel cada uno
Step-by-step explanation:
Hay 3 hermanos, si decimos que un pastel entero tiene 6 pedazos entonces su fraccion seria 6/6. Si dividimos este pastel entre los tres hermanos cada uno tendria...
[tex]\frac{6 / 3}{6}[/tex] = [tex]\frac{2}{6}[/tex]
Medio pastel seria la mitad de 6/6 que seria 3/6. Si dividimos esto entre los 3 hermanos cada uno tendria...
[tex]\frac{3 / 3}{6} = \frac{1}{6}[/tex]
Ahora que dividimos los 2 pasteles tenemos que unir las fracciones para saber cuanto pastel le toco a cada hermano...
[tex]\frac{2}{6} + \frac{1}{6} = \frac{3}{6}[/tex] o medio pastel cada uno
3 cm
20 cm
8 cm
5 cm
Find the lateral surface area of the solid above.
Answer:
320 cm sq
Step-by-step explanation:
Help please! I need asap
Answer:
b
Step-by-step explanation:
Answer:
B.137
Step-by-step explanation:
Its an obtuse angle
what is 5/6 -3/8 ........
Answer:
11 over 24 = 0.458
Step-by-step explanation:
who's your favorite grey's anatomy character?
Answer:
Mc Steamy
Step-by-step explanation:
please help me you will be my fav person ever if u do
Answer:
The answer are 1_ ASA
2_ SSS
3_ SAS
Please can someone help me I can’t fail this test
Answer:
x=7 y=4
Step-by-step explanation:
couldnt really see the question but i hope this helps
Out of the 96 customers at Jamie's boutique, 28 wore a size medium.
What is the probability that a randomly selected customer wore a size medium?
Answer:
7/24
Step-by-step explanation:
The probability would be 28/96, but we can simplify this fraction:
Divide 2 on both sides:
14/48
Divide 2 again:
7/24
So 7/24 is your answer! :) I hope I helped!
PQR is a right angled triangle calculate the size of angle marked x
Answer:
[tex]\displaystyle x \approx 37.4^\circ[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTrigonometry
[Right Triangles Only] SOHCAHTOA [Right Triangles Only] cosθ = adjacent over hypotenuseStep-by-step explanation:
Step 1: Define
Angle θ = x
Adjacent Leg = 5.8
Hypotenuse = 7.3
Step 2: Solve for x
Substitute in variables [Cosine]: [tex]\displaystyle cosx^\circ = \frac{5.8}{7.3}[/tex][Fraction] Divide: [tex]\displaystyle cosx^\circ = 0.794521[/tex][Equality Property] Trig inverse: [tex]\displaystyle x^\circ = cos^{-1}(0.794521)[/tex]Evaluate trig inverse: [tex]\displaystyle x = 37.39^\circ[/tex]Round: [tex]\displaystyle x \approx 37.4^\circ[/tex]A rectangular garden has a length of 8 feet and a width of 5 feet. The entire garden
is surrounded by walkway of uniform width. What does the algebraic expression
(2w+8)(2w+5) represent in this context?
A. the area of the garden only
B. the total area of the garden and walkway
C. the perimeter of the garden only
D. the perimeter of the walkway only
Answer:
b
Step-by-step explanation:
Using ABC, identify the ratio for sine of C
Answer:
BA / AC
Step-by-step explanation:
Given the triangle ABC;
To obtain the Sin C
Defining the attached triangle with respect to C:
Sine = opposite / hypotenus
Sin C = BA / AC
Hence, the ratio of sinC is BA /AC
2. What is 45% of 90?
O A. 40.5
OB 45
O 0.50
OD 200
Answer:
this would be the answer 40.5.
Take the 90 and multiply it by 45. Then multiply that by . 01.
What is the answer for x?
5=-2.5x+8
What is the value of the expression shown below? 2 over 3 to the power of 2 + 5 × 2 − 4 (4 points)
a 6 and 8 over 9
b 6 and 4 over 9
c 6 and 2 over 3
d 6 and 1 over 3
Answer: It equals 8.
Step-by-step explanation:
HELP URGENT PLEASE !!!!!!!!!!!!!!!!!!
Answer:
y=69*43
Step-by-step explanation:
this is not correct because the words are writen
A pair of shoes cost $75. This is $35 less than the cost of a pair of jeans write and solve an equation,Using n for the variable to find the cost of the jeans
Answer:
n=75 pair of shoes
n-75=35 equation
n=35+75=110
cost of jeans=110
What is the average rate of change for this quadratic function for the interval
from x= 1 to x = 3?
X
-5
5
-10+
Answer: -4
A P E X
Step-by-step explanation:
Find the slope!! Please
Answer:
The slope is -(1/3)
Step-by-step explanation:
For every 3rd step, the y-value decreases by 1 and the line intersects the y-axis in (0,1).
This observation yields the following equation for your line:
f(x) = y = -(1/3)x + 1
Therefore, the slope is -(1/3).
Use the graph of the polynomial function to find the factored form of the
related polynomial. Assume it has no constant factor.
A. (x + 1)(x-7)
B. (x + 1)(x + 7)
C. (x - 1)(x-7)
D. (x - 1)(x + 7)
The factored form of the related polynomial function is (x - 1)(x - 7).
What is polynomial function ?Polynomial function is a function that involves non-negative integer powers or positive integer exponents of a variable in an equation like the quadratic equation, cubic equation.
We have,
In the graph given in question, we can see that x - intercepts the axis twice.
And graphs behave differently at various x - intercepts. Sometimes the graph will cross over the x-axis at an intercept and other times the graph will touch the x-axis and bounce off.
Now, in graph;
The intercept at x = 1 ,
i.e. the solution of the x - 1 = 0 and passes through the axis.
Now,
The x - intercept at x = 7, is the solution of x - 7 = 0 and again passes through the axis.
So, from the above statements we can say that the factored form of the related polynomial is (x - 1)(x - 7)
Thus, we can say that the factored form of the related polynomial function is (x - 1)(x - 7).
Learn more about polynomial function from:
brainly.com/question/14711679
#SPJ1
Given that 3 apples and 4 pears cost $1.95, 4 pears and 1 orange cost $1.60, and 1 orange and 3 apples cost $1.15, what is the cost of 1 apple?
Answer:
Step-by-step explanation:
Given that 3 apples and 4 pears cost $1.95, 4 pears and 1 orange cost $1.60, and 1 orange and 3 apples cost $1.15, what is the cost of 1 apple?
Let us represent
Number of apples = x
Number of pears = y
Number of oranges = z
Given that
3 apples and 4 pears cost $1.95
3x + 4y = 1.95
4 pears and 1 orange cost $1.60
4y + z = 1.60
z = 1.60 - 4y
1 orange and 3 apples cost $1.15
z + 3x = 1.15
z = 1.15 - 3x
what is the cost of 1 apple?
Cole rides his bike to the ballfield starting from home. This
describes his trip:
A. Rides quickly downhill toward the field
B. Stops to wait for a friend
C. Rides slowly uphill toward the field
Drag a segment to each box to show the shape of the graph of
Cole's distance from home for each interval of time.
Describe the lines to chose as line 1 2 etc please
Answer: first line will be the on down the the right line 3... next the one with the straight line line 1 ..... then the fourth line slowly back upward
Step-by-step explanation:
Answer:
PartA: /
PartB: __
PartC: / its this one but less steeper(the second to last answer on the right)
Step-by-step explanation:
a(9b+13) in expanded form
Find the sum. Write your answer in simplest form. - 4 1/6 + 5 4/7
Answer:
1 17/42.
Step-by-step explanation:
Find the common denominator, which is 42.
So change -4 1/6 to -4 7/42.
And change 5 4/7 to 5 24/52.
So add -4 7/42 + 5 24/52 and you'll get: 1 17/42.
(The decimal form of this is 1.404762)
Question 1
Write an equation of the line parallel to y = –3x + 8 through (1, –4).
Question 2
Write an equation of the line perpendicular to y =1/3x – 5 through (–6, 2).