We will use Dirichlet's test to determine if the series converges. Let {an} and {bn} be the sequences defined as follows:
an = (-1)^(n+1) and bn = 1/n
Then, we can write the series as:
∑ (an * bn) = 1*(-1/1) - 1/2*(1/2) - 1*(-1/3) + 1/4*(1/4) + 1*(-1/5) - 1/6*(1/6) - ...
To apply Dirichlet's test, we need to show that:
The sequence {an} is bounded and monotonically decreasing.
The sequence of partial sums of {bn} is bounded.
For (1), note that |an| = 1 for all n and an is alternating in sign. Also, an+1 < an for all n, so {an} is monotonically decreasing.
For (2), note that the partial sums of {bn} are given by:
S_n = 1 + 1/2 + 1/3 + ... + 1/n
which is known as the harmonic series. It is well-known that the harmonic series diverges, but we can show that its partial sums are bounded as follows:
S_n = 1 + 1/2 + (1/3 + 1/4) + (1/5 + 1/6 + 1/7 + 1/8) + ... + (1/(2k-1) + 1/2k) + ... + 1/n
> 1 + 1/2 + 1/2 + 1/2 + ... + 1/2 + 1/n
= 1 + n/2n
= 3/2
Thus, the sequence of partial sums of {bn} is bounded by 3/2, and so Dirichlet's test implies that the series converges.
Therefore, the series 1 - 1/2 - 1/3 + 1/4 + 1/5 - 1/6 - 1/7 + ... converges.
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In the figure below, o ll g. Find the values of x and z. (42 - 16 • 1 84
Answer:
x = 96
z = 28
Step-by-step explanation:
Given:
(4z - 16) , 84, o║g
Proof
X = 180 - 84 (Sum of Opposite angles is 180)
x = 96
Let's take ∠(4z - 16) as ∠A
∠A = ∠X (Vertically opposite angles)
(4z - 16) = 96
4z = 96 + 16
4z = 112
z = 112/4
z = 28
Plzz answer fast guys
Answer:
(A)
Step-by-step explanation:
ZxZ-8=
Z-7
Note* Z-8=Z in the power of - 8 and Z-7=Z in the power of - 7
Answer:
z⁻⁷
Step-by-step explanation:
Use (zᵃ)ᵇ = zᵃᵇ and zᵃ * zᵇ = z⁽ᵃ⁺ᵇ⁾
The product of two consecutive positive integers is 56. Find the two integers
Answer:
Two consecutive integers are of the form
x and x + 1
Their product is equal to 56
x(x + 1) = 56
Solve and find the two numbers x and x + 1. The above equation may be written as follows
x2 + x - 56 = 0
Factor and solve
(x - 7)(x + 8) = 0
solutions: x = 7 , x = -8
x= - 8 is not valid since the number sought must be positive. Hence
x = 7 and x + 1 = 8 are the two consecutive numbers.
Step-by-step explanation:
...what's
[tex] \sqrt{169} [/tex]
Answer:
√169=13
Step-by-step explanation:
can also be understood by 13×13=169
Answer:
13
Step-by-step explanation:
√169 = 13
pls help if you know it
during a high school basketball game the home team scored 51 points and the opponent's score 62 points what is the point differential for (the difference between the number of points scored by a team and its opponent) for the home team?
-11
11
-10
10
Answer:
11
Step-by-step explanation:
just do 62-51=11 which gets you the difference between points
I really need help Please
Answer:
The tree was 5 feet when he bought it and it grew one foot every year.
I believe the equation would be h=t+5
Step-by-step explanation:
The answer would be h=t+5 because the height equals the year plus five.
Solve the system of linear equations
Answer:
There are infinite answers. it is the same line
Answer:
Infinite solutions
Step-by-step explanation:
<
10 of 21
Next >
- Lesson 5: Solving Any Linear Equation
Plymel
5.2: Trading Moves
Select another equation. Then take turns with each step
to solve the equation.
5x+7=x+13
O 2(x + 7) = -4x+14
Answer:
photo math is very helpful for math really try it
one of mr jones autographed baseballs is worth $55.00. if the value increases by 3% in the next year, what will be the new value of the baseball
Answer:
56.83?
Step-by-step explanation:
The new value of the baseball is $56.65.
Given that, the cost of baseballs = $55.00 and the value increases by 3% in the next year.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Now, new value = 55+3% of 55
= 55 + 0.03 × 55
= 55 + 1.65
= $56.65
Therefore, the new value of the baseball is $56.65.
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A group of friends were working on a student film that had a budget of $1200. They used $756 of their budget on props. What percentage of their total budget did they spend on props?
Answer: 63
Step-by-step explanation:
756/x = 1200/100
Cross multiply
75600 divided by 1200x
= 63
The percentage of budget used by them is 63%, the calculation is done by using the percentage used method.
Percentage-based problem:What information do we have?
Amount of budget = $1200
Amount of budget used = $756
Percentage of budget used = [Amount of budget used / Amount of budget]100
Percentage of budget used = [756 / 1200]100
Percentage of budget used = 63%
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Can you just get KA answers from somewhere Help me? pleases
Answer:
I went through khan academy and the answer is this.... Also what is your microsoft teams Account?
Step-by-step explanation:
Find the missing point of the following parallelogram.
A (6, 5)
B (5, 3)
C (2, 4)
D (7, 5)
I just took the test and the right answer is 6,5
Simplify the expression 9+(3x+4)
Answer:
3x+13
Step-by-step explanation:
=9+(3x+4)
=9+3x+4
=3x+13
What is the answer for g 3= g/3=-9
Answer:
1 = -9
Step-by-step explanation:
Just substitute 3 for g
then 3/3 = 1
find the domain and range of fx= 2-3sinx
Answer:
domain expansion
Step-by-step explanation:
jujutsu kaisen brúh
solve -3 (x + 1) - 2x= -6
A x=1
B x=5
C x = -7
D x = -9
Answer: C
Step-by-step explanation:
MATH PLS HELP
(7h+9)+(4h+4)
Answer:
11h+13
Step-by-step explanation:
7h+4h=11h
9+4=13
Answer:
11h+13
Step-by-step explanation:
Combine like terms.
Show that f(x) f(y) - f(x+y), where f(x)= [cos x - sin x o] [sin x cos x o] [o o 1]
Answer:
The answer is below
Step-by-step explanation:
Show that f(x) f(y) = f(x+y)
From trigonometric:
sin(x + y) = sinxcosy + cosxsiny
sin(x - y) = sinxcosy - cosxsiny
cos(x + y) = cosxcosy - sinxsiny
cos(x - y) = cosxcosy + sinxsiny
[tex]f(x)=\left[\begin{array}{ccc}cosx&-sinx&0\\sinx&cosx&0\\0&0&1\end{array}\right] ,f(y)=\left[\begin{array}{ccc}cosy&-siny&0\\siny&cosy&0\\0&0&1\end{array}\right] \\\\\\f(x)f(y)=\left[\begin{array}{ccc}cosxcosy-sinxsiny&-cosxsiny-sinxcosy&0\\sinxcosy+cosxsiny&-sinxsiny+cosxcosy&0\\0&0&1\end{array}\right] \\\\\\f(x)f(y)=\left[\begin{array}{ccc}cos(x+y)&-sin(x+y)&0\\sin(x+y)&cos(x+y)&0\\0&0&1\end{array}\right] \\\\\\[/tex]
[tex]f(x+y)=\left[\begin{array}{ccc}cos(x+y)&-sin(x+y)&0\\sin(x+y)&cos(x+y)&0\\0&0&1\end{array}\right] \\\\\\Therefore\ f(x)f(y)=f(x+y)[/tex]
I am not very good at math, and my daughter finished her math assignment and wasn't sure if she did everything correctly. Can someone make sure this is correct?
Answer:
I think its correct I don't know tho
Step-by-step explanation:
A rectangle is 2/5 inches long and
1/3 inches wide what is the area of the rectangle
Answer:
2/15 inches
Step-by-step explanation:
(2/5)*(1/3)=2/15in
In the number 8246315 what digit is in the hundreds place?
Answer:
the digit 3 is in the hundredths place
Step-by-step explanation:
8,246,315
the 3
Answer:
3
Step-by-step explanation:
six times the quantity two x plus three y
Answer:
12x + 18y
Lets first write the quantity "two x plus three y", this means, that we have x and y as unknowns. x is 2 times, so we have 2x; and y is 3 times, so he have 3y:
2x + 3y
Additionally we have that this quantity is six times, what means that it is multiplied by a number 6:
6(2x +3y)
If you like, we can apply the distributive property that means that given any three numbers a, b, c we have that a(b+c)=ab + ac. In our case a is 6, b is 2x and c is 3y. Thus, operating:
6(2x +3y) = 6*2x + 6*3y = 12x + 18y
So, "six times the quantity two x plus three y" is 12x + 18y
Step-by-step explanation:
Answer:
6(2x+3y)
Step-by-step explanation:
help me....................
Answer:
help me plssssssssssssss...
Answer:
it's 18+21 so 39
Step-by-step explanation:
anymore help ?
PLEASEE HELP ME I DONT KNOW HOW TO DO THIS !!
What is the least common multiple of 3, 2, and 9?
Answer:
18 is the LCM
solve -2(3x – 1)-2x = -3 – 5x + 13
Answer:
×=11
Step-by-step explanation:
-2(3×-1)-2=-3-5×+13
-6×-1-2×=-3-5×+13
-6×+2×+5×=1-3+13
1×=11
×=11
You need to cross a canal and want to determine the distance across the opposite side. Since you're able to take measurements on your side of the canal, you come up with 40 ft. and 16 ft. Find the distance x across the canal . Show all work
Answer:
36.7 ft
Step-by-step explanation:
Measurements for the sides of the canal is given as: 40 ft. and 16 ft.
You solve the above question using Pythagoras Theorem
The distance across the canal is calculated as:
√(40² - 16²)
= √(1344)
= 36.66060556 ft
Approximately = 36.7 ft
Therefore, the distance x across the canal = 36.7 ft
A cement truck pours cement into a container in the shape of a cylinder with a radius of 4 feet. The height, h, of the cement in the container increases at a rate of approximately 10 inches per minute. Write an equation that models the volume, V, of the cement in the container in terms of h, then use the equation to determine the time at which the volume is 80π cubic feet. Note that the volume of a cylinder is V=πr2h, where r and h are the radius and height of the cylinder.
Answer:
2009.6 and 13824 minutes and 230.4 hours
Step-by-step explanation:
v=3.14 x 4 x 2 x 80= 2009.6
Plz help me step by step explanation would help for work plzzzz And Thank you
Answer:
Step-by-step explanation:
5z=75
5z/5=75/5
z=15
cual es el opuesto de -5
Answer:
I think number 5