Enter the correct letter to match each summation expression with the property or formula.
Answers
Answer:
C B D E A
Step-by-step explanation:
The summation of integers with finite integral power (constant for all integers) up to a finite integer can be evaluated. The correct expressions filled would be in the sequence c,b,d,e,a.
How are positive integers summed upto a length with one, two and three degree power of each integer?Suppose we take the sum of natural numbers (also called positive integers) raised to power 1, 2, and 3, till the nth integer. Then, their sums are given as shown below:
[tex]S_1 = 1 + 2 + \cdots + n = \sum_{i=1}^n i = \dfrac{n(n+1)}{2}\\\\S_2 =1^2 + 2^2 + \cdots + n^2 = \sum_{i=1}^n i^2 = \dfrac{n(n+1)(n+2)}{6}\\\\S_3 = 1^3 + 2^3 + \cdots + n^3 = \sum_{i=1}^n i^3 = \left[\dfrac{n(n+1)}{2}\\\right]^2[/tex]
For this case, evaluating the rest of the two summations:
[tex]\sum_{i=1}^n ca_i = ca_1 + ca_2 + \cdots + ca_n = c(a_1 + a_2 + \cdots + a_n)\\\sum_{i=1}^n ca_i = c\sum_{i=0}^n a_i[/tex]
c was not depending on the variable on which summation is done, which was i. Therefore, it can come out directly.
Thus, whenever we get:
[tex]\sum_x k f(x)[/tex] where k is not depending on the value of x, then we can take it as:
[tex]\sum_x k f(x) = k\left(\sum_x f(x) \right)[/tex] (using the distributive property of multiplication over addition).
Similarly, we get:
[tex]\sum_{i=1}^n c = c + c + \cdots + c \text{ (n times)} = c\times n\\\sum_{i=1}^n ca_i = c.n[/tex]
Thus, the summation of integers with finite integral power (constant for all integers) up to a finite integer can be evaluated. The correct expressions filled would be in the sequence c,b,d,e,a.
Learn more about summation of integers raised to a power here:
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Related Questions
In the expression below n represents a whole number n x 3/4 Part A Select the statement below that describes the product The product is greater than N The product is less than N The product is equal to N Part B Explain your choice (This is a write in response.)
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Answer:
The product is less than N
Step-by-step explanation:
The expression is;
n * 3/4
Assuming N = 40;
40 * 3/4 = 30
The product is greater than N
This option is wrong because the product (30) is not greater than N
The product is less than N
This option is correct because the product (30) is not greater than N
The product is equal to N
This option is wrong.
if a triangle is dilated with a scale factor of 3, how is the perimeter of the triangle changed?
Answers
In ALMN, n = 73 cm, m = 89 cm and Angle M=61º. Find all possible values of Angle N, to the nearest degree.
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Answer:
46
Step-by-step explanation:
What is the distance between points (-4, 5) and (8, 40) on the coordinate plane?
SOME PLEASE HELP
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I attached a picture
Wesley's laundry basket has a rectangular base with an area of 200 square inches. The basket has a height of 24 inches and it is full of clothes. What is the volume of Wesley's laundry basket?
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Answer:
4800 cubic Inches
Step-by-step explanation:
Wesley's laundry basket has a rectangular base with an area of 200 square inches. The basket has a height of 24 inches and it is full of clothes. What is the volume of Wesley's laundry basket?
The volume of Wesley's Rectangular laundry basket = Area of the Base × Height of the basket
Base area = 200 square inches
Height of the basket = 24 inches
Volume of the basket = 200 square inches × 24 inches
= 4800 cubic Inches
Help (the answer isn't the 2nd one my friend did this test and chose that and got it wrong please )
Answers
Answer: 4 and 3/5
Step-by-step explanation:
Answer:
Really? The second one seems correct!
Step-by-step explanation:
Maybe they just switch the answers postions each time?
Example: You're friend picked the second one, but maybe that choice is not the second one that is showing on yours.
I might be wrong because I don't know how this works, but hope this helps and don't forget to follow!
please help, will be greatful :)
Answers
what level is this question?
Answer:
2.3cm
Step-by-step explanation:
We can see that it's a right triangle, similar to the one on the bottom left. Because the long side is 4 times longer, the short side is 4 times longer as well. So it's around
0.57cm*4= 2.28cm
Rounding to the 1st decimal place 2.3cm.
Please note, that rounding to 2 decimal places the answer 2.28cm could be inaccurate, e.g. if the real length would have been close to 0.574(9) or 0.565, but all of those options still round to 2.3cm.
i have to find the value of X, it’s in spanish:), and im trying to help a friend:)
Answers
answer is x = 10 degrees
Step-by-step explanation:
a right angle is 90 degrees. the angles added are 4x + 3x + 2x = 90.
so 9x = 90
divide by 9 on both sides
x = 10
-5x+y=-4 in function form
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Is it A,B,C,D y’all help me
Answers
Answer:
B
Step-by-step explanation:
It's a closed dot, so the sign will be less than or equal to 5.
Answer:
A
Step-by-step explanation:
SOMEONE PLEASE HELP
If f(x) = x2 is vertically stretched by a factor of 7 to g(x), what is the equation
of g(x)?
Answers
identify the diameter of a circle o.
Answers
Answer:
AC
Step-by-step explanation:
What is a diameter?
It is a line going straight through the center of the circle to the opposite side
So it is AC
2(x+9)=4(x+7)+2 what the answer?
Answers
Answer:
The answerrrrrrrrrrr is x=-6
Answer: =-2x - 8
Step-by-step explanation:
Shasta babysit for 4 and half hour and is paid how dose she get per hour and how much will she get in 8 hours
Answers
Answer:
how much does she get each hour
Step-by-step explanation:
Alan needs to read 4 novels each month Let N be the number of novels Alan needs to read in M months. Write an equation relating n to m. The use this equation to find the numbers of novels needs to read in 11 months.
Answers
Answer:
T=N*M and he needs to read 44 books.
Step-by-step explanation:
Note: Let T represent the total amount of books that Alan needs to read in 11 months.
If we plug in the information we have been given we will find the total:
T=N*M
T=4*11
T=44
Alan has to read 44 books within a 11 month period.
Please consider giving a thanks, a good rating, and Brainliest. It is always greatly appreciated! Thanks!
PLZ HELP GIVING ALL MY POINTS VERY URGENT
Answers
Answer:
88ft²
Step-by-step explanation:
Hey There
So first we want to find the area of the square
to do that we do 8x8 which equals 64
then we want to find the area of the triangle
to do so we multiply the base (8) and the height and divide that by 2
8x6=48
48/2=24
then we add the two together
24+64=88
88ft² is your answer :)
Answer:
hi I know that the other person already answered so I'm answering so u can give them brainliest
c::
What is 3/16 divided 3/8
Answers
Answer:
1/2 OR 0.5
Step-by-step explanation:
(*￣3￣)╭
Answer:
1/2
Step-by-step explanation:
Michael got a job peeling potatoes. In the first three hours of his shift, he peeled 84 potatoes. How many potatoes can he peel in seven hours?
A. 203
B. 196
C. 588
D. 168
Answers
How many 1 5 s are in 9?
Answers
Answer:
45
Step-by-step explanation:
To know how many 1/5 s are in 9, we will take the ratio of both numbers as shown;
9:1/5
= 9 ÷ 1/5
= 9 * 5/1
= 9 * 5
= 45
Hence there are 45 1/5s in 9
Systems of equations worksheet PLEASE HELP* 1-12
Answers
8. (-3,-13)
11. Y=4x+7
Can someone help me please
Answers
Answer:Alpaca.
traslaha
Step-by-step explanation:
Answer: c
Step-by-step explanation:
HELPPPPPPP PLEEASSSSEEE
Answers
Answer:
A would be at (-2,5) if reflected across the y axis
Answer:
(-2,5)
Step-by-step explanation:
Reflecting a point across the y axis mirrors it.
Pythagorean and theorem
1-6 thank you
Answers
f(x) = -7x - 2
g(x) = 3x2 + 4x – 5
Find: f(x) · g(x)
Answers
Answer:
wait what grade u in
Step-by-step explanation:
HELPPP!!
A radio station plays a variety of music to attract a large audience as possible. Each hour it plays 6 classic rock songs, 4 country songs, 5 pop songs, and 5 raps songs. What is the probability that the first song played will be a country song
Answers
If f(x)= 3x^3+4 find f(-3)
Answers
which one is the greatest 5/6 or 7/8 or 3/4
Answers
Answer:
im pretty sure its 7/8
Step-by-step explanation:
Answer:
It might be 7/8
Step-by-step explanation:
first which one would be greater
3/4 or 5/6 =? once you get you answer which one is greater?
5/6 or 7/8? so the answer will be .... 7/8
I NEED HELP ASAP! I give brainlist to whoever answers
The surface area of a cylinder is given by the formula SA = 2r2 + 2rh.
A cylinder has a radius of 9 cm and a surface area of 756 cm2.
Find the height of the cylinder.
Answers
Answer:
24 ^(2) - 10pi - 4cm 2 square centimeters
Step-by-step explanation:
hope this helps (:
Plzz answer this asap, question is in the picture.
Answers
Answer:
This is your answer
I need help with this please