Answer:
-2 is larger, -2>-5
For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate limn→[infinity]Sn to obtain the value of the series or state that the series diverges.
1) ∑[infinity]k = 1(1/k + 1 - 1/k + 2).
2) ∑[infinity]k = 1(1/(k + 6)(k + 7).
Answer:
The following are the solution to the given points:
Step-by-step explanation:
Given value:
[tex]1) \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\2) \sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}[/tex]
Solve point 1 that is [tex]\sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\[/tex]:
when,
[tex]k= 1 \to s_1 = \frac{1}{1+1} - \frac{1}{1+2}\\\\[/tex]
[tex]= \frac{1}{2} - \frac{1}{3}\\\\[/tex]
[tex]k= 2 \to s_2 = \frac{1}{2+1} - \frac{1}{2+2}\\\\[/tex]
[tex]= \frac{1}{3} - \frac{1}{4}\\\\[/tex]
[tex]k= 3 \to s_3 = \frac{1}{3+1} - \frac{1}{3+2}\\\\[/tex]
[tex]= \frac{1}{4} - \frac{1}{5}\\\\[/tex]
[tex]k= n^ \to s_n = \frac{1}{n+1} - \frac{1}{n+2}\\\\[/tex]
Calculate the sum [tex](S=s_1+s_2+s_3+......+s_n)[/tex]
[tex]S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....\frac{1}{n+1}-\frac{1}{n+2}\\\\[/tex]
[tex]=\frac{1}{2}-\frac{1}{5}+\frac{1}{n+1}-\frac{1}{n+2}\\\\[/tex]
When [tex]s_n \ \ dt_{n \to 0}[/tex]
[tex]=\frac{1}{2}-\frac{1}{5}+\frac{1}{0+1}-\frac{1}{0+2}\\\\=\frac{1}{2}-\frac{1}{5}+\frac{1}{1}-\frac{1}{2}\\\\= 1 -\frac{1}{5}\\\\= \frac{5-1}{5}\\\\= \frac{4}{5}\\\\[/tex]
[tex]\boxed{\text{In point 1:} \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2} =\frac{4}{5}}[/tex]
In point 2: [tex]\sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}[/tex]
when,
[tex]k= 1 \to s_1 = \frac{1}{(1+6)(1+7)}\\\\[/tex]
[tex]= \frac{1}{7 \times 8}\\\\= \frac{1}{56}[/tex]
[tex]k= 2 \to s_1 = \frac{1}{(2+6)(2+7)}\\\\[/tex]
[tex]= \frac{1}{8 \times 9}\\\\= \frac{1}{72}[/tex]
[tex]k= 3 \to s_1 = \frac{1}{(3+6)(3+7)}\\\\[/tex]
[tex]= \frac{1}{9 \times 10} \\\\ = \frac{1}{90}\\\\[/tex]
[tex]k= n^ \to s_n = \frac{1}{(n+6)(n+7)}\\\\[/tex]
calculate the sum:[tex]S= s_1+s_2+s_3+s_n\\[/tex]
[tex]S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(n+6)(n+7)}\\\\[/tex]
when [tex]s_n \ \ dt_{n \to 0}[/tex]
[tex]S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(0+6)(0+7)}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{6 \times 7}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{42}\\\\=\frac{45+35+28+60}{2520}\\\\=\frac{168}{2520}\\\\=0.066[/tex]
[tex]\boxed{\text{In point 2:} \sum ^{\infty}_{k = 1} \frac{1}{(n+6)(n+7)} = 0.066}[/tex]
The graph of f(x) = 0.5x is replaced by the graph of g(x) = 0.5x + k. If g(x) is obtained by shifting f(x) up by 5 units, then what is the value of k?
Answer:
k = 5
Step-by-step explanation:
The value of k is added to each y-coordinate, so represents the amount of up-shift. If the shift up is 5 units, then k=5.
Answer:
k = 5
Step-by-step explanation:
I got it right on the quiz
HELP!!!
on thursday, mabel handled 90 transactions. anthony handled 10% more transactions than mabel. cal handled 2/3 of the transactions that anthony handled, and Jade handled 16 more transactions than cal. how many transactions did jade handle?
Answer:
82
Step-by-step explanation:
Mabel = 90Anthony = 90 + 10% = 90 +90*0.1 = 99Cal = 2/3*99 = 2*33 = 66Jade = 16 + 66 = 82Which of the following statements best describes a theorem?
A. A theorem cannot be proven.
B. A theorem can be false.
C. A theorem is always true.
D. A theorem is never true.
Answer:
a
Step-by-step explanation:
A theorem cannot be proven.
What is the reciprocal of 9/2 and of 4/7 !pleasssee
Answer:
2/9 and 7/4(or 1 3/4)
Step-by-step explanation:
A reciprocal is just the original number flipped.
Expand and simplify
(2x2 + 3)(4x + 5) - 8x(x - 2)
A study was done by an online retail store to determine the rate at which users used its website. A graph of the data that was collected is shown: A line graph with Number of Months on the x axis and Number of Users, in thousands, on the y axis. The x axis has a scale from 0 to 36 with an increment of 4. The y axis has a scale of 0 to 60 with increments of 6. A straight line connecting 0, 0 and approximately 36, 54 is drawn. What can be interpreted from the range of this graph? v
Answer:
A graph of the data that was collected is shown: A line graph with Number of Months on the x axis and Number of Users, in thousands, on the y axis. The x axis has a scale from 0 to 36 with an increment of 4. The y axis has a scale of 0 to 60 with increments of 6. A straight line connecting 0, 0 and approximately 36, 54 is drawn. What can be interpreted from the range of this graph? v .
Answer:
c
Step-by-step explanation:
Robert is building model cars as well as model trains. The cars take 4 hours to build while the trains take 6 hours
to build. He is hoping to build as many as possible before the next model fair exhibition. If he has 100 free hours
until the fair, how many can he build? Write the inequality for this problem. Let cars be the domain and trains the
range.
10 cars and 10 trains in 100 hours
it approximately take him 10 hours to build one car and one train how 6+4=10 how many times can 10 go into 100 10 times hope this helps a little
An airplane descends 1.4 miles to an elevation of 7.15 miles. fund the elevation of the plane before its descent
Answer:
The plane's starting elevation was 6.75 miles
Step-by-step explanation:
Answer:
no its 9.15
Step-by-step explanation:
x − 1.4 = 7.75
+ 1.4 + 1.4 Add 1.4 to both sides.
x = 9.15
Calculate the distance between (6 − 5i) and ( 1 + 3i).
A: /113
B: /29
C: /53
D: /89
Answer: D
Step-by-step explanation:
i just had this question on a quiz and it said the correct answer was /89
A soccer ball with a diameter of 8.6 inches is shipped in a box that is a square prism and has a side length of 9.5 inches. How much volume is available to be filled with packing material if the shipping company wants the box completely full? Round your answer to the nearest tenth.
524.5 in^3
774.2 in^3
5,115.8 in^3
1805.6 in^3
1190.2 in^3
Answer:
A 524.5 in^3
Step-by-step explanation:
**LOOK AT PHOTO** Whats the answer and what are the steps?
Answer:
[tex]a=2K-b[/tex]
Step-by-step explanation:
[tex]K=\frac{a+b}{2}[/tex]
Switch sides:
[tex]\frac{a+b}{2}=K[/tex]
Multiply both sides by 2:
[tex]\frac{2\left(a+b\right)}{2}=2K[/tex]
[tex]a+b=2K[/tex]
Subtract b from both sides:
[tex]a+b-b=2K-b[/tex]
[tex]a=2K-b[/tex]
6(x + 3) =6x + 18
is what kind of property?
Answer: Distributive Property of Multiplication.
Step-by-step explanation:
Please help! If x = 6 and b = 4, what is x+b
Hey there!
ANSWER: [tex]10[/tex]EXPLANATION:If you want to know how to solve, you will need to find the value of x and y. x is equal to 6 and b is equal to 4.
[tex]x(6)+b(4)=?[/tex]
So we basically just add 6 and 4.
[tex]6+4=10\\x+b=10(Answer)[/tex]
Hope this helps!
[tex]-TetsedHyperr[/tex]
There are 450 seats in a theatre. 48% of the seats are occupied. How many seats are not occupied?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{234}}}}}[/tex]
Step-by-step explanation:
Total seats in a theatre = 450
Finding the total occupied seats
[tex] \dashrightarrow{ \sf{48\% \: of \: 450}}[/tex]
[tex] \dashrightarrow{ \sf{ \frac{48}{100} \times 450}} [/tex]
[tex] \dashrightarrow{ \sf{216}}[/tex]
Finding the seats that are not occupied
[tex] \longrightarrow{ \sf{450 - 216 = 234}}[/tex]
Hope I helped!
Best regards! :D
If simplifying the following problem, what
would be the correct first and third
steps?
8 - 4 [5(2-2)] + 3
Answer: First step would be doing the () first. The third step would be 4 times 0. I think so, forgive me if I’m wrong.
Step-by-step explanation:
The translation rule is (x,y) (x+_,y+_)
Answer:
see below
Step-by-step explanation:
The question is not clear but I will provide info based on given
Translation of
(x, y) → (x + a, y+ b)means sliding by a points to left/right and by b points to up/down
The flow-rate of your current sink faucet is 2.7 gallons per minute. If you purchase a fancy low-flow faucet for $294, the flow rate would decrease by 39%. Assuming you use your faucet for an average of 1,558 minutes per month and water costs $0.006 per gallon, compute the payback period (in months) of such a purchase.
Answer:
23
Step-by-step explanation:
Write the word form of the following decimals. 432.98
Answer: Four hundred and thirty two point nine - eight.
Step-by-step explanation:
Hey there! I'm happy to help!
With the numbers before the decimal, you just say it normally. After the decimal, you just name the digits.
So, you would call this number four hundred thirty-two point nine eight.
Have a wonderful day! :D
4. When rounding to the nearest ten and the nearest hundred, what number rounds to 400? a-295, b-299, c-390, d- 399
Answer:
c. and d.
Step-by-step explanation:
c when tenth
d when hundreth
Answer: D
Step-by-step explanation: D because it is closest to 400 out of the other 3 choices.
The perimeter of a rectangular window is 43 feet. The width of the window is 5 ft more than the length. Find the width of the window
Answer:
13.25 ft
Step-by-step explanation:
Let w represent the width of the window. Then w-5 represents the length, and the perimeter is ...
P = 2(L+W)
43 = 2((w-5) +w) = 4w -10
53/4 = w = 13.25 . . . feet
The width of the window is 13.25 ft.
You can multiply -2.2 by 6.2 to find the total variation in the water level.What decimal represents the total variation in water level Ericka observed?
Answer:
-13.64 millimeters
Step-by-step explanation:
just use a calculator ._.
Write a function that takes the base and height of a triangle and return its area.
//Method/function name is areaOfTriangle
//Return type is double
//Method receives two parameters of type double - base and height
public static double areaOfTriangle(double base, double height){
//Find the area using the formula: 1/2 * base * height
double area = 0.5 * base * height;
//return the area
return area;
} //End of areaOfTriangle method
Step-by-step explanation:The function above has been written in Java.
It contains comments explaining each line of the code. Please go through the comments.
In order to test the function, a complete program containing a main method has also been written. This is shown as follows;
//Class definition begins
public class Area{
//Method/function name is areaOfTriangle
//Return type is double
//Method receives two parameters of type double - base and height
public static double areaOfTriangle(double base, double height){
//Find the area using the formula: 1/2 * base * height
double area = 0.5 * base * height;
//return the area
return area;
} //End of areaOfTriangle method
//Write the main method to call the method
public static void main(String []args){
//Call the areaOfTriangle() method in the main method
//Set the base to 12 and the height to 6
System.out.println(areaOfTriangle(12, 6));
}
} //End of class definition
Sample Output>> 36.0
Eli is making smoothies. Each smoothie uses 1/2 cup of yogurt. How much yogurt does he need to make 20 smoothies?
Answer:
40 smoothies
Step-by-step explanation:
if a 1/2 is one then times it by two
Answer:
40 smoothies
Step-by-step explanation:
a) The newbom baby, Jake, needs some supplies. Jake's mom gave you this ist of
things he needs. You and your friend have agreed to spend $115 of the $300 on
Jake. You spend 15% of it on a new blanket 25% of it on toys, and 40% of ton
clothes. How much money do you have left to spend on diapers for Jake?
Solve y over negative 6 + 5 = 9. (1 point)
This should be your equation - (y/-6) + 5 = 9
Answer:
y/-6 = 4 <y = -24 <
Answer:
[tex]y=-24\\[/tex]
Step-by-step explanation:
Write the equation
[tex]\frac{y}{-6} +5=9[/tex]
Subtract 5 from both sides
[tex]\frac{y}{-6} =4[/tex]
Multiply both sides by -6
[tex]y=-24\\[/tex]
Hope this helps! : )
the line plot shows the ages at which a group of musicians started to play an instrument based on the line plot which statement is not true
Answer:
Their are 34 musicians
Step-by-step explanation:
If you count the chart you will see that the number of X's equals 34
Answer:
34
Step-by-step explanation:
I did this too, just count the x's
Hope this helps!
Use S = n^2 to find the sum of 1 + 3 + 5 + . . . + 701.
Answer:
123201
Step-by-step explanation:
This is an arithmetic sequence of common difference 2 and starting value 1,
So we can use the formula for an arithmetic sequence if we know what is the order of the last term.
Then first use the formula for the nth term to find "n":
[tex]a_n=a_1+(n-1)d[/tex]
where d = 2, first term = 1 and last term = 701
[tex]a_n=a_1+(n-1)d\\701=1+(n-1)*2\\700=(n-1)*2\\350=n-1\\n = 351[/tex]
Knowing this, we can estimate the partial sum:
[tex]S=n\,\frac{a_1+a_n}{2} \\S=351\,\frac{1+701}{2} \\S=351\,*\,351\\S = 123201[/tex]
Find the derivative of the function. y = sin−1(6x + 1)
If you don't know the derivative of the inverse of sine, you can use implicit differentiation. Apply sine to both sides:
[tex]y=\sin^{-1}(6x+1)\implies\sin y=6x+1[/tex]
(true for y between -π/2 and π/2)
Now take the derivative of both sides and solve for it:
[tex]\cos y\dfrac{\mathrm dy}{\mathrm dx}=6[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=6\sec y[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac6{\cos\left(\sin^{-1}(6x+1)\right)}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac6{\sqrt{1-(6x+1)^2}}[/tex]
Eight avocados cost $4.
How much do 16 avocados cost?
How much do 20 avocados cost?
How much do 9 avocados cost?
16 avocados costs = $8, 20 avocados costs = $10 and 9 avocados costs = $4.5
What is the Cost?The amount of money that a company spends on the creation or production of goods or services.
Given that, Eight avocados cost $4.
Therefore, each of them costs = 4/8 = 1/2
So, 16 avocados = 16*1/2 =$8
20 avocados = 20*1/2 =$10
9 avocados = 9*1/2 =$4.5
Hence, 16 avocados costs = $8, 20 avocados costs = $10 and 9 avocados costs = $4.5
For more references on Cost, click;
https://brainly.com/question/15135554
#SPJ2
