Answers
Answer:
Option (a) [tex]\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}[/tex]
Step-by-step explanation:
The given expression is :
[tex]\dfrac{3}{1{\cdot} 2}+\dfrac{3}{2{\cdot} 3}+\dfrac{3}{3{\cdot} 4}+\dfrac{3}{4{\cdot} 5}+....[/tex]
We need to rewrite the sum using sigma notation.
The numerator is 3 in all terms.
At denominator, in first term (1)(2), in second term (2)(3) and so on.
A general term for the denominator is k(k+1).
Sigma notation is :
[tex]\sum_{k=1}^{\infty} \dfrac{3}{k(k+1)}[/tex]
Hence, the correct option is (A).
Related Questions
Which of the following represents an inequality statement with a solution of
Please help out I’ll give you brainliest
Answers
Answer:
the second to last one
Step-by-step explanation:
Sorry if it is incorrect!
Will give brainliest please help
Answers
Answer:
49
Step-by-step explanation:
In the middle of the figure , there's a square whose each side length is 7. So area of the square will be [tex] {7}^{2} = 49 \: {unit}^{2} [/tex]
GIVING BRAINLIEST AND STARS
13)
Using a map scale of 1/2 inch = 10 miles, what would be the distance on the map between two cities that are actually 120 miles
apart?
A)
6 inches
B)
8 inches
C)
10 inches
D)
12 inches
Answers
Answer:
A) 6 Inches
Step-by-step explanation:
1/2=10 to find how many inches we need to get 120 miles, you have to find the conversion rate.
Conversion rate is 120 ÷ 10 which equals 12.
Now we multiply the conversion rate (12) times 1/2 to get an answer of 6 inches.
i'd appreciate a brainliest :)
Round 33,500 to the nearest 1000.
Answers
Answer: 34,000 (Since it's 500, it rounds up)
I hope this helps, and Happy Holidays! :)
At a bake sale, as student spent $11.00 buying 3 brownies and 5 cookies. His friend spent $3.95 buying 1 brownie and 2 cookies. What is the price of a brownie?
Answers
Answer:
$[tex]$2.25[/tex]
Step-by-step explanation:
Let [tex]b =[/tex] the cost of one brownie, [tex]c =[/tex] cost of one cookie
[tex]3b + 5c = 11[/tex]
[tex]b+2c = 3.95[/tex]
Times [tex]3[/tex] on both sides on the second equation above to get the following:
[tex]3b + 6c = 11.85[/tex]
[tex]3b+6c - (3b+5c) = 11.85-11[/tex]
[tex]3b+6c-3b-5c = 0.85[/tex]
[tex]c = 0.85[/tex]
To find the value of [tex]b[/tex], use substitution:
[tex]b+2c = 3.95[/tex]
[tex]b = 3.95-2c[/tex]
[tex]= 3.95 - 2\times0.85[/tex]
[tex]= 2.25[/tex]
[tex]\therefore[/tex] the cost of a brownie is $[tex]$2.25[/tex]
Hope this helps :)
Can someone help me with 3 and 4
Answers
Answer:
x÷3+10 (if x=15)
15÷3+10
5+10
15
Use a power-reducing formula to rewrite the given expression in terms of the first power of the cosine:
tan^2(8x)
Answers
tan²(8x) = sin²(8x) / cos²(8x)
… = (1 - cos²(8x)) / cos²(8x)
… = 1 / cos²(8x) - 1
… = 2 / (1 + cos(16x)) - 1
where the last equality follows from the half-angle identity for cosine,
cos²(x) = (1 + cos(2x)) / 2
HELP GIVEING BRAINLIST What is the solution set of -11 > 1 + a?
a > -10
a -12
a < -10
a < - 12
Answers
Answer:
the solution set is -11 > 1 + a?
a > -10
a -12
a < -10
If QRST is a kite, find the measure of QRS
Answers
Answer:
!!!!
137°
i took the test and that was the right answer.
Step-by-step explanation:
QRST is a kite therefore, the value of angle QRS in the kite is 137 degrees.
Properties of a kiteOne pair of opposite angles is equal.Diagonals are perpendicular to each other.The sum of angles in the kite is 360 degrees.
Therefore,
79 + 79 + 11x - 6 + 4x + 13 = 360
158 - 6 + 13 + 11x + 4x = 360
158 + 7 + 15x = 360
15x = 360 - 158 - 7
15x = 195
divide both sides by 15
x = 195 / 15
x = 13
Therefore,
∠QRS = 11(13) - 6 = 143 - 6 = 137 degrees.
learn more on kite here:https://brainly.com/question/3087585
#SPJ2
which statement is true regarding the graphed functions?
Answers
Answer:
if -2 refers to the y-intercept "f(-2)=g(-2)" would be correct
Dkendbdjdbebdbdbdjdnd
Answers
Answer:
5/2
Step-by-step explanation:
The 5^-3 and 5^6 cancel out to be 5^3. Then the 5^3 cancels out with the 5^2 in the denominator and leaves you with just a 5. The 2^2 makes the 2^3 in the denominator just 2. So, you are left with 5/2! Hope this helps.
Write the following ratio in simplest form 8 to 12
Answers
Answer:
2/3 or 2 to 3
Step-by-step explanation:
Good luck!
y = 230x + 100
Is this proportional or non proportional?
Answers
Proportional equations are of the form y = kx, for some fixed constant k. The k value is the constant of proportionality.
The +100 at the end is why we don't have a proportional equation.
Visually all proportional equations go through the origin, meaning the lines have y intercept of 0. For y = 230x+100, the y intercept is 100.
Help me pleaseeeeeeeeeeeeeeeeee
Answers
find the area of each trapezoid 32 ft x 16 ft 18 ft
Answers
Answer:
A = 432 ft^2
Step-by-step explanation:
[tex]A=\frac{a+b}{2} *h[/tex]
A = (32+16)/2 * 18
A = 48/2 * 18
A = 24*18
A = 432 ft^2
Which of the following is equivalent to 75/100? A 2/3 B 10/15 C 25/50 D 15/20
Answers
Answer:
D. 15/20
Step-by-step explanation: Because if it is 100 divide by 5 then it equals 20 and since 75% is 3/4 then 15/20 is your answer.
Answer:
D 15/20
Step-by-step explanation:
b=9 c=4 bc+12.3=?
AAAAAAAAAAAAAAAAAAAAAAAAAASAP
Answers
Answer:
48.3
Step-by-step explanation:
since b = 9 and c = 4
9 x 4 = 36 and 36 + 12.3 = 48.3
Carrie has 18 pens. Carrie has 2 more than 4
times the number of pens that Patricia has.
Exactly how many pens does Patricia have?
Answers
Answer: ( sorry I misread the problem)
I'm not sure what I'm supposed to be multiplying with
but I'll try my best
subtract 2 with 18 and divide 4 with the remaining
18 -2 = 16
then it is 16/4= 4
Pat has a total of 4pens
Which of these tables represents a function?
Answers
Answer:
W
Step-by-step explanation:
The table that will represent a function is the table where every x-value (domain) has exactly one y-value (range).
Table W represents a function because each x-value has exactly only one y-value.
The other tables have two y-values assigned to a one x-value.
Answer:
W
Step-by-step explanation:
Please help me 20 points!!!!!
Answers
Answer:
A. 0.4 km
B. 48 fruits to 12 vegetables
C. 72 hours
60%
Step-by-step explanation:
1 km = 1000 m
You have 400 m
1000m/1km = 400m/1000m
400/1000
0.4km
4:1
Ok so an easy way to do this one is multiplication.
you need the number of fruits to be 4 times more than the number of vegetables.
A would be 2:1 because 16 is 2 times more than 8
B would be 4:1 because 48 is 4 times more than 12
C would be 8:1 because 24 is 8 times more than 3
D would be 3:1 because 60 is 3 times more than 20
B would be the correct answer
If they traveled 216 miles in 3 hours, to find average you have to divide miles by hours.
216/3
72 hours
The tigers won 12 of their last 20 games.
12/20
0.6
Percent is 100 times the decimal.
0.6*100
60%
Don't be afraid to reach out with any more questions! I hope this helps!
At home, Alice noticed that she had a flat tire. With the spare, Alice drove 30 miles to the next shop at 45 mph. After getting the new tire, she drove home at 70 mph. What was Alice's average speed for her round trip?
Answers
Answer: Approximately 54.7826 mph
As a fraction, this average speed is exactly 1260/23 mph.
========================================================
Work Shown:
"Alice drove 30 miles...at 45 mph". This means
t = d/r
t = 30/45
t = 2/3
She drove for 2/3 of an hour, which is (2/3)*60 = 40 minutes.
Then "she drove home at 70 mph". She drove the same distance, meaning,
t = d/r
t = 30/70
t = 3/7
She drove for 3/7 of an hour, which is roughly (3/7)*60 = 25.714 minutes.
------------------------------
Add up the time values
(2/3 hr) + (3/7 hr)
(2/3 + 3/7) hr
(14/21 + 9/21) hr
23/21 hr
She spent 23/21 of an hour driving going to the auto shop and then back home. The total distance she traveled was 30+30 = 60 miles.
Use these values to find the speed
r = d/t
r = d divided by t
r = 60 divided by (23/21)
r = (60/1) divided by (23/21)
r = (60/1) * (21/23)
r = (60*21)/(1*23)
r = 1260/23
r = 54.7826
Her average speed for the round trip is about 54.7826 mph.
The area of a rectangle is 36 square meters. If the length of the rectangle is 3, what is the width?
a
12
b
15
c
108
d
9
Answers
So, 36/3 = 12
Width is 12
What is the quotient of 228 ÷ 12?
Answers
Answer:
19
Step-by-step explanation:
228/12=19
************************
Answers
Answer: I think i my be wrong but i thing its B
Step-by-step explanation:
A quiche took 101 minutes to make and 175 minutes to bake. Estimate the combined time it took to prepare the quiche by rounding to the nearest ten first and then adding the rounded numbers.
Answers
Answer:
1233
Step-by-step explanation:
kieley
Answer:
80
Step-by-step explanation:
180-100+80.
21. Which property is used to simplify the expression 5(3x + 18) to 152 + 90?
Can you answer this?
Answers
Marla sold 12 baseball caps for a total of $39, including tax. The equation. 12c=39 can be used to find c, the cost of one cap. What is the value of c
Answers
Answer:
$3.25
Step-by-step explanation:
12c = 39
12/12 =0
39/12 = 3.25
c = 3.25
Geoff earns $9.25 per hour before taxes, and he works 40 hours per week. Geoff's employer withholds (takes out) 10.65% of geoff's income for taxes. What are geoff's total weekly earnings after taxes are withheld?
A) $ 39.41
B) $59.90
C) $ 330.60
D) $ 370.00
Answers
Answer:
a
Step-by-step explanation:
A man travels 320 miles in 8 hours. If he continues at the same rate, how many miles will he
travel in the next 2 hours?
Answers
Answer: 80 miles
Step-by-step explanation:
320miles/8hours= 40mph
40mph=xmiles/2hrs
40*2= 80 miles
what is the correct factorization of x^2 - 2x - 15?
Answers
Answer:
Step-by-step explanation:
x2 - 2x - 15
x2 - 5x + 3x - 15
x(x - 5) + 3(x - 5)
(x - 5) and (x + 3) are the factors
if this needs to be solved further, you will need to set both of these equations equal to 0.
x-5=0 and x+3=0
this will give you x=5 and x=-3
i hope this helped :)