[tex]\boxed{\sf \lim_{n \to \infty} (\frac{1}{1-n^2}+\frac{2}{1-n^2} +...\: \frac{n}{1-n^2} }[/tex]
- Need a step-by-step answer!
- Thank you!
[tex]\\ \sf\Rrightarrow \lim_{n\to \infty}\left(\dfrac{1}{1-n^2}+\dfrac{2}{2-n^2}\dots \dfrac{n}{1-n^2}\right)[/tex]
Take LCM as 1-n^2[tex]\\ \sf\Rrightarrow \lim_{n\to \infty}\left(\dfrac{1+2+3\dots n}{1-n^2}\right)[/tex]
1+2..n=n(n+1)/2[tex]\\ \sf\Rrightarrow \lim_{n\to \infty}\left(\dfrac{\dfrac{n(n+1)}{2}}{1-n^2}\right)[/tex]
[tex]\\ \sf\Rrightarrow \lim_{n\to \infty}\dfrac{n(n+1)}{2(1-n^2)}[/tex]
[tex]\\ \sf\Rrightarrow \lim_{n\to infty}\dfrac{n(1+n)}{2(1-n)(1+n)}[/tex]
[tex]\\ \sf\Rrightarrow \lim_{n\to \infty}\dfrac{n}{2(1-n)}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{\infty}{2-\infty}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{-1}{2}[/tex]
[tex]{\sf \lim_{n \to \infty} (\frac{1}{1-n^2}+\frac{2}{1-n^2} +...\: \frac{n}{1-n^2}) } \\ = {\sf \lim_{n \to \infty} (\frac{1 + 2 + ..n}{1-n^2})} \\ = {\sf \lim_{n \to \infty} ( \frac{n(n + 1)}{2} \div 1 - {n}^{2} )} \\ = {\sf \lim_{n \to \infty} ( \frac{n(n + 1)}{2} \times \frac{1}{ 1 - {n}^{2}} )} \\ ={\sf \lim_{n \to \infty} ( \frac{n(n + 1)}{2(1 - {n}^{2} )} )} \\ = {\sf \lim_{n \to \infty} ( \frac{n(n + 1)}{2 (1 - n )(1 + n) } )} \\ = {\sf \lim_{n \to \infty} ( \frac{n(1 + n)}{2 (1 - n )(1 + n) } )} \\ = {\sf \lim_{n \to \infty} ( \frac{n}{2 (1 - n )} )} \\ = {\sf \lim_{n \to \infty} ( \frac{n}{2 - 2 n } )} \\ = \sf \frac{ \infty }{2 - \infty } \\ = \frac{ - 1}{2}
[/tex]
Answer:
[tex] \frac{ - 1}{2} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
sub duplicate ratio of 16:9 is
The sub duplicate ratio of 16:9 is
4: 3
Sub duplicate ratiosThe sub-duplicate ratio is found by finding the square root of both the numerator and denominator
The given ratio is 16:9
Find the square root of 16
[tex] \sqrt{16} = 4[/tex]
Find the square root of 9
[tex] \sqrt{9} = 3[/tex]
Combining the two square roots that were found, the sub duplicate is:
[tex] \frac{4}{3} [/tex]
Therefore, the sub duplicate ratio of 16:9 is
4: 3
Learn more on sub duplicate of ratios here: https://brainly.com/question/25881746
6. Line a: y - 3x = 4
Line b: y = 3x + 5
Line c: y - 4x = 3
Which lines are parallel
Answer:
Line a and b
Step-by-step explanation:
the function f(x)= (x-8) (x+2) (x+3) has which zeros
Answer:
(8, 0)
(-2, 0)
(-3, 0)
Step-by-step explanation:
x - 8 = 0
x = 8
x + 2 = 0
x = -2
x + 3 = 0
x = -3
[tex](x-8)(x+2)(x+3) =0\\\\\implies x -8 =0~~~ \text{or}~~~x+2 =0 ~~~ \text{or}~~~x+3 = 0\\\\\implies x = 8 ~~~~~~~~ \text{or}~~~~~~x = -2 ~~~ \text{or}~~~ x = -3\\\\\\\text{Hence the roots are}~ 8, -2 ~\text{and} ~-3[/tex]
if l||m, find the value of x.
Answer:
9
Hope you could get an idea from here.
Doubt clarification - use comment section.
Answer:
Step-by-step explanation:
11x - 47 = 6x - 2 Corresponding angle. Add 47 to both sides
11x = 6x + 47 - 2 Combine
11x = 6x + 45 Subtract 6x from both sides
11x - 6x = 45 Combine
5x = 45 Divide by 5
5x/5 = 45/5
x = 9
if the lines that comprise a system of equations have two different y-intercepts, is it possible that the system has infinitely many solutions?
Answer:
No, it is not possible.
Step-by-step explanation:
A system of linear equations with infinitely many solutions must meet at every single point. That means they have both the same y-intercept and the same slope. If either one of those are different, there cannot be infinitely many solutions.
Write 5.4 as a mixed number and as an improper fraction.
Write your answers in simplest form.
Answer:
5.4 as a fraction is 27/5.
Step-by-step explanation:
Learned in 5th grade
how to turn 18/48 into the power of 10 please tell the answer as soon as possible, it's for my semester
Point Q is plotted on the coordinate grid. Point P is at (20, −30). Point R is vertically above point Q. It is at the same distance from point Q as point P is from point Q. Which of these shows the coordinates of point R and its distance from point Q?
Point R is at (−40, 30), a distance of 60 units from point Q
Point R is at (−40, −10), a distance of 20 units from point Q
Point R is at (−40, −30), a distance of 60 units from point Q
Point R is at (−40, 10), a distance of 20 units from point Q
Answer:
Point R is at (−40, −30), a distance of 60 units from point Q
Step-by-step explanation:
Correct option is ,
Point R is at (-40, 30) , a distance of 60 units from Point Q.
hope this answer helps you dear take care!
Daniel runs at a pace of 8 miles in 60 minutes. What is his pace per mile?
Answer:
60/8 = 7.5 mins per mile
Step-by-step explanation:
WILL GOVE 50 POINTS AND BRAINLIEST PLZZZZZZZZZZZZZZZZZ HELP
Examine the diagram of a chloroplast.
Which choice best describes the function of the part labeled B?
enclosed space containing proteins used in ATP formation
membranes enclosing open space
layered stacks of membranes
fluid space that contains DNA, ribosomes, and other enzymes
Answer:
fluid space that contains DNA, ribosomes, and other enzymes
Step-by-step explanation:
B is points towards the "empty" space, meaning its Stroma.
Stroma defintion: involved in the synthesis of organic molecules from carbon dioxide and water or the fluid of the chloroplast surrounding the thylakoid membrane;
Let's look at the answer choices.
A. enclosed space containing proteins used in ATP formation
B. membranes enclosing open space
C. layered stacks of membranes
D. fluid space that contains DNA, ribosomes, and other enzymes
Obviously not C.
A is Synthase.
B is the whole thing.
It is D.
(BTW THIS IS MATH!! Not science!! Just in case you have more questions!)
Answer:
raw
Step-by-step explanation:
If a dozen exercise books cost 144, what will 14 of the same books cost
Need help quick !!!!!!!
write an equation for the nth term of the arithmetic sequence.then fine a10
Answer is attached.
Hope it helps :)
what is the 5th multiple of 6
Answer:
30
Step-by-step explanation:
What is 6, 5 five times?
Or 5x6?
a breakfast cereal advertizes that it has 5g of fibre in every 30g serving. How much fibre would someone receive if he or she ate a 50g serving of that cereal?
Answer:
8.33... grams of fiber
Step-by-step explanation:
The grams per serving is 5/30 or 1/6 or .166... or 16.66...%.
So Fiber = 16.66% * serving size or
F = 16.66 * 50 = 8.33...
PLS HELP WILL MARK YOU BRAINLIEST!!
No fake answers pls
Answer:
1. =
Step-by-step explanation:
1.
R.H.S
5.2 + 5.a
(now taking 5 common)
5(2+a)
In a bag, the ratio of red to blue counters is 3:4.
If 3 red counters are removed the ratio of red to blue counters becomes 3:5.
How many blue counters are there in the bag?
a drilling team detected water 38 feet below the ground. if it took workers 8 days to be able to dig and pull up the water, how much did they dig each day on average? What do the x and y intercepts represent?
Answer:
On average, the workers dig 4.75ft each day. Also, what x and y questions?
Step-by-step explanation:
Take [tex]38/8=4.75[/tex]
I hope you have a great day and make me the brainliest.
The drilling team digs 4.75 feet every day, as per the given conditions, and y and x-intercept represent the depth and days respectively.
Given that,
A drilling team detected water 38 feet below the ground. if it took workers 8 days to be able to dig and pull up the water,
the equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
The total depth of dig = 38 feet
Total time took to dig 38 feet = 8 days
For 1 day, the depth of the dig = 38 / 8 = 4.75
Now,
Let x is the number of days,
while y be the depth left to dig in feet,
y = 38 - 4.75x
The drilling team digs 4.75 feet every day, as per the given conditions, and y and x-intercept represent the depth and days respectively.
Learn more about equations here:
brainly.com/question/10413253
#SPJ2
In IJK, i = 40 inches, j = 80 inches and ZK=92°. Find ZJ, to the nearest degree.
Answer:
61.9
Step-by-step explanation:
mark me as brainliest
Answer:
62°
Step-by-step explanation:
The law of cosines is used to find the length of side k:
k² = i² +j² -2i·j·cos(K)
k² = 40² +80² -2·40·80·cos(92°) ≈ 8223.3568
k ≈ 90.6827 . . . . . . . take the square root
Then the law of sines is used to find angle J.
sin(J)/j = sin(K)/k
J = arcsin(j/k·sin(K)) = arcsin(80/90.6827·sin(92°)) ≈ 61.84°
J ≈ 62°
Find the inverse function. f(x) = (x + 1
Answer:
( x + 1 ) ^ 3
Step-by-step explanation:
f(x) = 3√x - 1
replace x with y
x = 3√y - 1
solve for y,
x = 3√y - 1
x^3 + 3x^2 + 3x + 1 = (x+1)^3
HOPE THIS HELPS :)
ASAP
Please show working out I will give out brainiest :)
Winnie Bracken opened a savings account at Dallas Trust Bank on March 1. It pays 4% interest compounded quarterly. She opened her account with initial deposit of $10,000. She made $1,000 deposits at the end of each quarter. How much is in the account at the end of 6 quarters?
The compounded interest is applied to the amount in the account at end
of a period specified in the rate of compounding.
The amount in the account at the end of 6 quarters is approximately $16,767.2Reasons:
The interest paid on the account = 4% compounding
Amount with which she opened the account = $10,000
Amount she makes as deposit at the end of each quarter = $1,000
Therefore;
The interest per quarter = 4% ÷ 4 = 1%
Amount in the account after the end first quarter, A₁, is therefore;
A₁ = 10,000 × 0.01 + 10,000 + 1,000 = 11,100
The amount in the second quarter, A₂, is given as follows;
A₂ = 11,100 × 0.01 + 11,100 + 1,000 = 12211
A₃ = 12211 × 0.01 + 12211 + 1,000 = 13333.11
A₄ = 13333.11 × 0.01 + 13333.11 + 1,000 = 14466.4411
A₅ = 14466.4411 × 0.01 + 14466.4411 + 1,000 = 15611.105511
At the end of the 6th quarter, we have;
A₆ = 15611.105511 × 0.01 + 15611.105511 + 1,000 = 16767.2165991
The amount in the account at the end of 6 quarters, A₆ ≈ $16,767.2
Learn more about compounding interest rate here:
https://brainly.com/question/8806008
Find the value of r in the isosceles triangle shown below.
8
8
6
Answer:
r = 6
.....................
What is the y intercept of the line y + 11=-2(x+1.5)
[tex]y +11 = -2(x+1.5)\\\\\implies y = -2x -3 -11\\\\\implies y = -2x - 14\\\\\text{The above equation is in a form of y = mx +b,}~\text{where}~~ b = -14~\text{ is the y-intercept.}[/tex]
Someone please help me with this I learned this in class of the day I don’t remember it
In the equation = + , what does b represent?
Answer:
Although the equation is incomplete (b doesn't appear), I'll venture a guess that the correct equation looks something like this:
y = 2x + b [or y = mx+b]
b is the y-intercept.
Step-by-step explanation:
In the format of y = 2x + b, b represents the y-intercept (the value of y when x = 0).
Pleas help me for B and C
Answer:
In no b 7 people has represented □
In no c 2 people referred giraffe than dogs
Answer:
(b)Total 8 complete square in given pictogram represented 64 people.
(c) 6 more people preferred giraffes than dogs.
Fill in the blanks with the answer to each question based on information provided.Two toy robots are having a race. Robot A can go 14 meter in 15 seconds. Robot B can go 1 meter in 50 seconds.1) If Robot A continues at that same speed, how long will it take to go 1 meter? Remember units! __________2) How long for Robot A to go 4 meters at that speed? Remember units! _________
Answer:
1 1/14 seconds4 2/7 secondsStep-by-step explanation:
We are being asked for times, so we can express the rate in terms of seconds per meter.
(15 seconds)/(14 meters) = (15/14) seconds per meter = 1 1/14 seconds/meter
__
1) It will take Robot A 1 1/14 seconds to go 1 meter.
2) it will take Robot A 4 2/7 seconds to go 4 meters. (4 times as long)
given the following measures of the side of triangles, which is a right triangle?
Answer:
Step-by-step explanation:
Essentially, we can use the pythagorean rule that:
a^2+b^2=c^2
c^2 resembles the hypotenuse, which is almost always the largest number. therefore, we simply have to find two which equal the largest side:
9^2+40^2=41^2
81+1600=1681
1681=1681
Based on this math, A is our right angle!
Hope this helps!
please try looking at the picture :(( i’m really struggling so much!!
Answer:
4- true
5-true
6-false
7-false
8-true
9-true
Step-by-step explanation:
Follow the letters and the sign of congruence
≅