[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.
NEED HELP ASAP 40 POINTS GEOMETRY QUESTION PLEASE GIVE FULL ANSWER!!!Which of the lines listed below is perpendicular to the line with the equation
Answer:
Step-by-step explanation
Which expression has been solved with the following number line?
Answer:
Step-by-step explanation:
Add 116 to 123 and then subtract it by the larger number and 323
Simplify the expression:
10v + -5 + 7
Answer:
10v + 2
Step-by-step explanation:
Answer:
10v + 2
Step-by-step explanation:
Ok, so when were adding varibles, whenever theres the same varible, we add them. In this case we have v and numbers. -5+7 is 2 because -5 and positive 5 cancel eachother out so were left with 2 from the 7. now the equation is 10v+2!
The grass in Jamie's yard grew 16 centimeters in 10 days. It was growing at a constant rate.How many days did it take the grass to grow 1 centimeter?How many centimeters did the grass grow in 1 day
Answer:
Step-by-step explanation:
16 cm / 10 days = 1.6 cm/day
10 days / 16 cm = 0.625 days/cm
Jane wrote all the natural numbers from 1 to 12. including 1 and 12.
how many numbers did Jane write?
Answer:
12 numbers
Step-by-step explanation:
1,2,3,4,5,6,7,8,9,10,11,12
Prism A and Prism B have the same volume. Which could be the dimensions of Prism B?
Prism A:
length = 8 feet
width = 4 feet
height = 5 feet Prism B:
length=? feet
width=? feet
height=? feet
Answer:
length = 20 ftwidth = 20 ftheight = 0.4 ftStep-by-step explanation:
The volume of Prism A is ...
V = LWH
V = (8 ft)(4 ft)(5 f) = 160 ft³
Any set of dimensions that have a product of 160 ft³ will give a prism with the same volume. You could have, for example, ...
length = 20 ft
width = 20 ft
height = 0.4 ft
Step-by-step explanation:
We know that
Volume of prism = lwh
=> 8 × 4 × 5
=> 32 × 5
=> 160 ft³
So,
The possible length, height and width could be
Length = 10 ft
Breadth = 8 ft
Height = 2 ft
please help what is 4.651-50.3
Jacob says that (12 + 31) × 5 is
equivalent to 12 + 31 x 5 because of the
associative property.
Describe the associative property
in words.
Determine if Jacob is correct. Justify
your answer.
Answer:
Step-by-step explanation:
the associative property means that when you are adding OR multiplying you can group the numbers however you want
Jacob is wrong because (12 + 31) x 5 = 215 and 12 + 31 x 5 = 167
Find y such that the slope between (2, y) and (5, -3) is 7.
Answer:
y= -24
Step-by-step explanation:
since the slope is 7 the value of y should decrease as the value of x decreases. and since you went back 3 on the x, you should go down 21 on the y resulting in -3-21 which is -24
what is the answer to 5x+1=3x+7
Answer:
Step-by-step explanation:
5
+
1
=
3
+
7
5x+1=3x+7
Solve
1
Subtract
1
1
from both sides of the equation
5
+
1
=
3
+
7
5x+1=3x+7
5
+
1
−
1
=
3
+
7
−
1
5x+1{\color{#c92786}{-1}}=3x+7{\color{#c92786}{-1}}
2
Simplify
Subtract the numbers
Subtract the numbers
5
=
3
+
6
5x=3x+6
3
Subtract
3
3x
from both sides of the equation
5
=
3
+
6
5x=3x+6
5
−
3
=
3
+
6
−
3
5x{\color{#c92786}{-3x}}=3x+6{\color{#c92786}{-3x}}
4
Simplify
Combine like terms
Combine like terms
2
=
6
2x=6
5
Divide both sides of the equation by the same term
2
=
6
2x=6
2
2
=
6
2
\frac{2x}{{\color{#c92786}{2}}}=\frac{6}{{\color{#c92786}{2}}}
6
Simplify
Cancel terms that are in both the numerator and denominator
Solution
=
3
please help me asapppp
ty :)
Answer:
C. 3
y = 3x - 4
Step-by-step explanation:
y = 3x - 2
Slope stays 3 because they are parallel.
y - 5 = 3(x - 3)
y - 5 = 3x - 9
y - 5 + 5 = 3x - 9 + 5
y = 3x - 4
Step-by-step explanation:
y= 3x-4
hopefully that is helpful
Simplify 2^3 x 2^18
Answer:
2^21
Step-by-step explanation:
3+18=21
Answer:
2/27
Step-by-step explanation:
Here is me work:
There are fewer than 30 students in the A-level mathematics class. One half of them
play the piano, one quarter play hockey and one seventh are in the school play.
How many of the students play hockey?
The number of students that play hockey is 7
The proportion is given as:
[tex]Piano =\frac 12[/tex]
[tex]Hockey =\frac 14[/tex]
[tex]School\ Play =\frac 17[/tex]
The total number of students must be a multiple of 2, 4 and 7 less than 30;
The only multiple of 2, 4 and 7 less than 30 is 28.
The number of students that play hockey is the product of 28 and the proportion that plays hockey.
So, we have:
[tex]Hockey =\frac 14 \times 28\\[/tex]
Multiply
[tex]Hockey =7[/tex]
Hence, 7 students play hockey
Read more about common multiples at:
https://brainly.com/question/290451
Find the coefficient of z^3 in -7xy^2z^3
Answer:
z^3 in -7xy^2z^3 = -117649/1 = -117649
Step-by-step explanation:
I think sorry if wrong
How I can answer this question, NO LINKS, if you answer correctly I will give u brainliest!
Answer:
It is the first one.
Which of the following is in the range of the function based on the input-output table below?
Answer:
A.
Step-by-step explanation:
The answer is A because first:
1. we are looking for y so B and D are off the table
2. It goes from least to greatest so C is also gone
3. You are left with A
Answer:
A
Step-by-step explanation:
The range is the y value.
In this table the y value is pay per month.
How I can answer this question, NO LINKS, if you answer correctly I will give u brainliest!
Answer: 54 words does Rachel type per minute
Step-by-step explanation:
Rachel types 162 words in 3 minutes Rachel types at a constant rate.
We have to find how many words does Rachel type per minute.
By definition of unit rate: all we do is divide 162 by 3 which gives us 54
Answer:
54 words per minute
Step-by-step explanation:
In 3 minutes Rachel types 162 words
Then
In 1 minutes,Rachel types 162÷3 words
In 1 minutes Rachel types 54 words
.
. . Rachel types 54 words per minute
what is10 + 9
i really dont know
can someone help me
[tex] \huge \green{ \boxed{ANSWER}}[/tex]
[tex]10 \: + \: 9 \: = {\boxed{19}}[/tex]
USE CALCULATOR -_-
[tex] \mathfrak{JazmineChoi}[/tex]
STAN TREASURE
Answer:
19
Step-by-step explanation: 10 +9 = 19
How do I find a solution in an equation
Answer:
How to find a solution in an equation:
(1) Substitute the number for the variable in your equation,
(2) Simplify the expressions on both sides of your equation and
(3) Determine whether the resulting equation is true. If it is true, the number is a solution. If it is not true, the number is not a solution.
Step-by-step explanation:
If any questions, please ask them below.
If you have no questions, please have a great rest of your day/night!
whats 5 plus 6, i cant find out, its hard
Answer:
its 11
Step-by-step explanation:
because when you add 6 and 5 your answer will be 11 and its very easy and clear
Given a parabola with the
vertex located at (-2,5) and there
is another point on the parabola
located at (3,7), What is the
equation of the parabola in Vertex
form?
Answer:
The equation is 2/25(x + 2)^2 + 5.
Step-by-step explanation:
WE can write the vertex form as
y = a(x - b)^2 + c where a is some constant and (b, c) are the coordinates of the vertex.
So here we have:
y = a(x + 2)^2 + 5
As (3, 7) is a point oin the curve:
7 = a(3 + 2)^2 + 5
7 = 25a + 5
a = 2/25.
Can u please help me solve this much appreciated
There are 10 pens in a box. There are x red pens in the box. All the other pens are blue. Jack takes at random two pens from the box. Find an expression, in terms of x, for the probability that Jack takes one pen of each colour. Give your answer in its simplest form.
The probability that one of each color is selected is [tex]\frac{10x - x^2}{45}[/tex]
ProbabilitiesThe probability of an event is the chances of the said event
The given parameters are:
Total = 10Red = xBlue = 10 - xCalculating the required probabilityThe probability that one of each color is selected is calculated as follows:
[tex]P = P(Blue) \times P(Red) + P(Red) \times P(Blue)[/tex]
So, we have:
[tex]P = \frac{10 - x}{10} \times \frac{x}{9} + \frac{x}{10} \times \frac{10 - x}{9}[/tex]
This gives
[tex]P = \frac{x(10 - x)}{90} +\frac{x(10 - x)}{90}[/tex]
Take LCM
[tex]P = \frac{2x(10 - x)}{90}[/tex]
Simplify the above expression
[tex]P = \frac{x(10 - x)}{45}[/tex]
Expand
[tex]P = \frac{10x - x^2}{45}[/tex]
Hence, the probability that one of each color is selected is [tex]P = \frac{10x - x^2}{45}[/tex]
Read more about probabilities at:
https://brainly.com/question/7965468
The following is a conversion table for hours and minutes. Which numbers belong in the hours column?
1, 2, 3
1, 2, 4
2, 3, 4
2, 5, 6
Answer:
2,3,4
Step-by-step explanation:
numbers that equal to 39
Answer:
1 , 3 , 13 , and 39
Step-by-step explanation:
1 x 39 =39
3 x 13 = 39
13 x 3 = 39
39 x 1 =39
Answer:
Step-by-step explanation:
The product 3*13 equals 39. This is in addition to the identity 1*39 = 39.
why didnt lawrenece fishburn play morpheus in matrix 4 reddit
Answer:
I'm confused about your question can you explain?
please help me figureout 4y+x=8
the output is two more than the input
Help, please! I need this done for my finals.
Answer:
First one is yes second one is yes 3 one is yes 4 one is yes and first one is a repeating decimal
Step-by-step explanation:
Also sorry if it's wrong but I tried also hope u have a great day!
What’s the missing angle of 121 and 29
Answer:
I am going to guess that shape you are trying to find is an triangle
30˚
Step-by-step explanation:
A triangle angle is 180˚
So add 121 and 29
Which is 150
180 - 150 which is 30
So the missing angle is 30˚
Hope this helps!