The sum of the series is ∑n=1^∞ an = S∞ = 7.
(a) We have the formula for the partial sums:
Sn = ∑n=1[infinity]an
And we know that:
SN = 7 - (9 / N^2)
So we can find the value of a1 by taking N to infinity:
S∞ = lim(N→∞) SN = lim(N→∞) (7 - (9 / N^2)) = 7
a1 = S1 - S0 = S1 = 7 - S∞ = 0
Now we can use the formula for partial sums to find the other two sums:
∑n=1^{10}an = S10 - S0 = (7 - (9 / 10^2)) - 0 = 6.91
∑n=4^{16}an = S16 - S3 = (7 - (9 / 16^2)) - (7 - (9 / 3^2)) = 6.977
Therefore, ∑n=1^{10}an = 6.91 and ∑n=4^{16}an = 6.977.
(b) We can find a3 using the formula for partial sums:
S3 = a1 + a2 + a3
We know that a1 = 0 and we can find S3 from the formula for partial sums:
S3 = 7 - (9 / 3^2) = 6
So we have:
a3 = S3 - a1 - a2 = 6 - 0 - a2 = 6 - a2
We don't have enough information to determine a2, so we cannot determine the exact value of a3.
(c) We can find a general formula for an by looking at the difference between consecutive partial sums:
Sn - Sn-1 = an
So we have:
a1 = S1 - S0 = 7 - S∞ = 0
a2 = S2 - S1 = (7 - (9 / 2^2)) - 7 = -1/4
a3 = S3 - S2 = (7 - (9 / 3^2)) - (7 - (9 / 2^2)) = 1/9 - 1/4 = -7/36
We can see that the denominators of the fractions are perfect squares, so we can make a guess that the general formula for an involves a square in the denominator. We can then use the difference between consecutive terms to determine the numerator. We get:
an = -9 / (n^2 (n+1)^2)
(d) To find the sum of the series, we can take the limit of the partial sums as n goes to infinity:
S∞ = lim(n→∞) Sn
We can use the formula for the partial sums to simplify this expression:
Sn = 7 - (9 / n^2)
So we have:
S∞ = lim(n→∞) (7 - (9 / n^2)) = 7 - lim(n→∞) (9 / n^2) = 7
Therefore, the sum of the series is ∑n=1^∞ an = S∞ = 7.
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Help me plz i will give brainlest
Answer:
the answer should be (3,-2)
Please I need help
Write the equation for a parabola with a focus at (1,-4) and a directrix at x = 2.
X=?
Answer:
Step-by-step explanation:
The directrix is a vertical line, so the parabola is horizontal. The focus lies to the left of the directrix, so the parabola opens to the left.
For a left-opening parabola:
x = a(y-k)²+h,
a < 0,
vertex (h,k)
focal length p = 1/|4a|
focus (h-p, k)
directrix: x=h+p
Apply your data
focus (1,-4)
directrix x=2
vertex (1.5,-4).
focal length p = 0.5
a = -1/|4p| = -½
x = -½(y-2)²+ ½
The translation shown in the graph moves the figure to the right. What kind of translation is shown?
the figure go to the left
Mrs. Brownstone brought 56 liters of juice for the fifth grade party. How many milliliters of juice did she bring?
Answer:
56000 milliliters
1 liter = 1000 milliliters
56(1000)=56000
Step-by-step explanation:
Can someone help me, I forgot how to solve this
Answer:
y = mx + b
Step-by-step explanation:
Which is Better Lion ling action movie or The Cartoon Version? Explain your answer gets 25 Points!
Answer:
Cartoon
Step-by-step explanation:
Answer:
The cartoon lion king is way better. I say this because the action one is kinda creepy. I feel like Disney tried too hard to make it great, that it ended up not as good as it could be.
Step-by-step explanation:
Hope this is good enough!
Help help help help help help help help help
Answer: a: 23.4
Step-by-step explanation:
Answer:
A.23.4
Step-by-step explanation:
first find the volume of the tank 18x12x25=5400 then find how many gallons of water tank can hold 5400/231=23.4
hope this helps have a blessed day :)
what is domain and range because I got it wrong is not the right one
Answer:
You most likely got it wrong because you didn't plot all the points that are actually in the table, the domain and range are both right.
PLZ HELP ME PLZ I NEED IT
Answer:
Step-by-step explanation:
The intersection occurs at the point (3,-3) so those are the coordinates.
Daniel debe $12.300 a Miguel y paga con un billete de $50.000 ¿cuanto dinero le devuelven ?
Answer:
37,700
Step-by-step explanation:
I believe that you do 50,000 - 12,300. That would get you to your final answer of 37,700. So Miguel has to give 37,700 back to Daniel.
Hope this helped you!
Answer:
Miguel devuelve a Daniel $ 37.70
Step-by-step explanation:
50 - 12.3 = 37.7
Damian’s computer repair shop earned $2,500 in income last week. Expenses were $2,750. What was Damian’s profit or loss for the week?
Answer:
2500-2750 = - 250
hence,he lost $250
a cylindrical tank has a radius of 3 m and a height of 12 m.
What is the volume of the tank?
Answer:
Volume = 339.12 m^3
Step-by-step explanation:
Volume = Pi(r^2)(height)
Volume = 3.14(3^2)(12)
Volume = 339.12 m^3
Solve 11=h-14 please
Answer:
25
Step-by-step explanation:
25-14=11
Answer:
25
Step-by-step explanation:
11=25-14
Since 11+14 is 25 then h in 11=h-14 must be 25
Jada’s dog was 5 1/2 inches tall when it was a puppy. Now her dog is 14 1/2 inches taller than that. How tall is Jada’s dog now as a fraction?
Answer: 20 or 20/20
Step-by-step explanation: It equals a whole number.
Answer:
20/20
Step-by-step explanation:
so there is 5 1/2, you can add 14 1/2, 14 plus five equals 19, but you also have to add the two halves, which in total gives you 20/20.
X/4=8
Solve that using the opposite operation
Answer:
x = 32
Step-by-step explanation:
4 • (x/4) = 8 • 4
x = 32
Step-by-step explanation:
[tex]\qquad\sf\dashrightarrow x/4=8 [/tex]
[tex]\qquad\sf\dashrightarrow x=4×8 [/tex]
[tex]\qquad\sf\dashrightarrow x=32 [/tex]
Find the degree of the following polynomial:
7xy223 + 8y5 – 3x4 + 4
Answer:
224
Step-by-step explanation:
polynomial degree:224
leading term:7x^223
leading coefficient:7
answer quickly and quietly incorrectly please
Answer:
Your answer is
A & E
Mark my answer as brainlist . I need that urgently . Folow me for more answer.
Step-by-step explanation:
Which expression is equivalent to 1/4(12x + 16) + 3x + 7
Please help!!!
a. 15/4x + 7
b. 15x + 23
c. 6x + 23
d. 6x + 11
Answer:
the answer is 6x+11
Step-by-step explanation:
1/4(12+16)+3x+7
1/4×4(3x+4)+3x+7
(3x+4)+3x+7
3x+4+3x+7
6x+11
If
f(x) = x^2 + 2x - 4
and
g(x) = 3x + 1
Find
f(g(x)) = ?
Answer;
f (x) = 2x-4g (x) =x^2
Step-by-step explanation:
The solution is 9x² + 12x - 1
The composition function f ( g ( x ) ) is 9x² + 12x - 1
What is Composition of functions?
Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
Given data ,
Let the first function be represented as f ( x )
The value of f ( x ) = x² + 2x - 4
Let the second function be represented g ( x )
The value of g ( x ) = 3x + 1
Now , the composition function f ( g ( x ) ) is calculated by
Substitute the value of x as 3x + 1 , in f ( x ) , we get
f ( g ( x ) ) = f ( 3x + 1 )
f ( 3x + 1 ) = ( 3x + 1 )² + 2 ( 3x + 1 ) - 4
On simplifying the equation , we get
f ( 3x + 1 ) = ( 9x² + 6x + 1 ) + ( 6x + 2 ) - 4
f ( 3x + 1 ) = 9x² + 12x - 1
Therefore , the value of f ( 3x + 1 ) is 9x² + 12x - 1
Hence , the composition function f ( g ( x ) ) is 9x² + 12x - 1
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The pair of figures is similar. Use proportions to find the value of each variable.
The age at which a person can be tried as an adult
Answer:
giyi
Step-by-step explanation:
Find angle a.
You will get 20 points
Answer:
127
Step-by-step explanation:
15+38+a=180
a= 127
Mary has a large sum of money to deposit, but since she has heard many stories from her grandmother about the Great Depression, when many banks lost their customers’ deposits, she is worried that the bank might not keep her money safe. Give Mary some recommendations about what she can do to make sure that her money stays protected.
Mary should make sure to choose a bank that is FDIC insured. Furthermore, if she has more than maximum deposit insurance amount to deposit, she should spread her deposits out among several separate banks. These should be totally different banks, not simply different branches of the same bank. The FDIC will insure up to the maximum deposit insurance amount at each bank, even if the bank fails.
The masses of 4 containers loaded on a ship are 28 tonnes,45 tonnes,16.8tonnesand 48500kg .What is 5he total mass in tones?
Step-by-step explanation:
first of all we have to change kg into ton= 48500kg into ton =53.462ton(48500/907.168)
after that we add all the weight of 4 container = 28+45+16.8+53.462
total will be his total mass of tones he had =143.262
Which are equivalent to 32 · 34 ? Check all that apply.
36
38
96
3-4 · 310
30 · 38
33 · 33
(3 · 2) · (3 · 4)
(3 · 3) · (3 · 3 · 3 · 3)
Using exponential properties, it is found that the equivalent expressions are given by:
[tex]3^6[/tex].[tex]3^{-4} \times 3^{10}[/tex][tex]3^0 \times 3^8[/tex].(3 · 3) · (3 · 3 · 3 · 3)What happens in the multiplication of two terms with the same base and different exponents?We keep the base and add the exponents, that is:
[tex]a^b \times a^c = a^{b + c}[/tex]
In this problem, we want an expression equivalent to:
[tex]3^2 \times 3^4 = 3^{2 + 4} = 3^6[/tex]
The equivalent expressions have the same result, hence, they are:
[tex]3^6[/tex].[tex]3^{-4} \times 3^{10}[/tex][tex]3^0 \times 3^8[/tex].(3 · 3) · (3 · 3 · 3 · 3)More can be learned about exponential properties at https://brainly.com/question/234372
3^6 Or A
3^-4 · 3^10 or C
3^3 · 3^3 Or E
(3 · 3) · (3 · 3 · 3 · 3) Or H
Pls consider me for Brainliest!!
Find the slope!!!
Quickly please
Answer:
the slope is m= 2
Answer:
2
Step-by-step explanation:
Slope is (y1 - y2) / (x1 - x2) for any 2 respective x's and y's.
For any of the points here, you get 2.
HELPPPPPPP pleaseeeee mathhhh
9514 1404 393
Answer:
y = 1/6x
Step-by-step explanation:
The constant of proportionality is the ratio of y to x:
k = y/x
Using the point you have circled, it is ...
k = 2/12 = 1/6
Then the equation y = kx can be written:
y = 1/6x
The selling price of an item is $600. It is marked down by 30%, but this sale price is still marked up
from the cost of $350. Find the markup from cost to sale price.
The markup is $ (Round to the nearest dollar as needed.)
Answer:
7000
Step-by-step explanation:
divide 600 and 30 then multiply that answer by 350
Answer:
Correct answer is 70 trust me
Step-by-step explanation:
Choose the equations that are equivalent. Select all that apply.
A. 52 = 8n +4
B. 42n + 1) = 52
C. 4 = 52 - 8n
D. 4n = 48
Answer:
A. 52 = 8n +4
C. 4 = 52 - 8n
A car corporation produced 1980 fewer cars this month than last.
Write a signed number to represent this month's change in production.
Answer:
there was 1300 fewer cars so your answer would be -1300 :-)