by mathematical induction 1.2²+2.3²+.....+n(n+1)(n+2)(3n+5)/12​

Answers

Answer 1

Step-by-step explanation:

1.2+2.3+3.4+⋯+n(n+1)=∑k=1nk(k+1)

=∑k=1n(k2+k)

=∑k=1n(k2)+∑k=1n(k)

=n(n+1)(2n+1)6+n(n+1)2

=n(n+1)6(2n+1+3)

=n(n+1)6(2n+4)

=n(n+1)6[2(n+2)]

=n(n+1)(n+2)3


Related Questions

find the output when x = 6

Answers

Answer:

5

Step-by-step explanation:

the points is also given on graph

(6,5)

Pretty sure it’s 5.

i-Ready
Practice: Add and Subtract Rationals - Quiz - Level G
what number makes the equation true

Answers

Answer: the answer is -2 1/3

Step-by-step explanation: it would be -2 1/3 because 5 + 2=7 and then add the 1/3 to make -7 1/3

The number that makes the equation

[tex]\rm -5 +x = -7\dfrac{1}{3}[/tex]     true is [tex]\rm \bold {-2\dfrac{1}{3} }[/tex].

So option 4 is correct.

Let the number that makes equation true is x

The question is that what makes equation true

[tex]\rm -5 +x = -7\dfrac{1}{3}[/tex]

This equation is a linear expression with one variable and rational numbers.

This equation can be solved in the following way

[tex]\rm -5 +x = -\dfrac{22}{3} \\x = 5 -\dfrac{22}{3} \\x = (15-22)/3 \\x = -7/3\\ x= -2\dfrac{1}{3}[/tex]

So from the given options in figure  we can see that option 4 is correct

For more information please refer to the link given below

https://brainly.com/question/15815501

1. Cuando compras un automóvil y lo sacas del concesionario, este comienza a
depreciar. Mira adquirió un automóvil por $18,645, y tiene un valor residual de
$1,950 y una vida útil de 7 años. ¿Cuál es el porcentaje de depreciación del costo de
auto por año? Indica si consideras que la oferta es conveniente para Mima y explica
tu respuesta
Identifica los datos y establece la relación entre estos.
b. Resuelve la relación, presentando el procedimiento y contesta la pregunta en
una oración completa.​

Answers

El porcentaje de depreciación de la auto de Mira por año es del 12,79 %.

Cómo calcular el valor de depreciación del auto de Mira por año?

Para calcular el valor de depreciación del auto de Mira debemos tener en cuenta la siguiente información:

Precio del auto nuevo: $18,645Precio residual de auto: $1,950Vida útil de auto: 7 años.

De acuerdo a la información anterior, debemos calcular cual es la diferencia entre el precio nuevo y el precio residual.

$18,645 - $1,950 = $16,695

Ahora, para saber el valor de depreciación por año dividimos este valor ($16,695) en 7.

$16,695 ÷ 7 = $2,385

Por ultimo para saber el porcentaje de depreciación por año realizamos el siguiente procedimiento:

$18,645 ÷ 100 = $186.46$2,385 ÷ $186.46 = 12,79%

Aprenda más de depreciación en: https://brainly.com/question/16933803

You have $2,000 on a credit card that charges a 17% interest rate. If you want to pay off the credit card in 3 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?

Answers

Answer:

Step-by-step explanation:

2000*17%=340

2000+340=2340

2340/4*12= 48.75

Please help I really need help

Answers

Answer:

D

Step-by-step explanation:

integers are a whole number; a number that is not a fraction.

What is a density of an object that has a mass of 100g and a volume of 20cm3

Answers

Answer:

5g/cm^3

Step-by-step explanation:

DENSITY=mass/volume

=100/20

=5g/cm^3

So the density is 5g/cm^3

Based on your measurements in question 1, what is the relationship between the diagonals of parallelogram ABCD

Answers

Answer:

Point E divides each diagonal in half. It is the midpoint of  AC and BD . This means the two diagonals bisect each other at point E.

Step-by-step explanation:

PLATO

Answer:

Point E divides each diagonal in half. It is the midpoint of  AC and BD . This means the two diagonals bisect each other at point E.

Step-by-step explanation:

edmentum

Richard invests $230.92 every month into his mortgage. At the end of 30 years, he has a balance of $184,033.06. What interest did he make over 30 years?

Answers

The answer is $101,233.06

Richard made $100,719.46 in interest over 30 years on his mortgage.

To calculate the total interest Richard made over 30 years, we need to find the total amount he invested and then subtract that from the final balance.

Richard invests $230.92 every month for 30 years, which is a total of:

Total investment = 30 years * 12 months/year * $230.92/month

Total investment = $230.92 * 360

Total investment = $83,313.60

Now, we can calculate the interest earned by subtracting the total investment from the final balance:

Interest = Final balance - Total investment

Interest = $184,033.06 - $83,313.60

Interest = $100,719.46

Therefore, Richard made $100,719.46 in interest over 30 years on his mortgage.

To know more about interest:

https://brainly.com/question/30393144?

#SPJ2

3³ - (60 - 10) + 8

Answers

Answer:

According to the Google calculator, the answer is -15

Maria, Bill, and Eric have a total of $95 in their wallets. Maria has 10 less than Bill. Eric has 3 times what Bill has. How much does each have?
Plz help.

Answers

Answer:

[tex] \boxed{Maria \: got \: \$11} \\ \boxed{Bill \: has \: \$21} \\ \boxed{ Eric \: has \: \$63}[/tex]

Step-by-step explanation:

[tex]let \: maria \: be \to \: m \\ let \: eric \: be \to \: e \\let \: bill \: be \to \: b \\then : m =b - 10 \: and \: e = 3b \\ but : m + b + e = 95 \\ hence \to \: (b - 10) + b + (3b) = 95 \\ 2b - 10 + 3b = 95 \\ 5b = 95 + 10 \\ 5b = 105 \\ \boxed{b = 21} \\ m = b - 10 = 21 - 10 \\ \boxed{ m = 11} \\ e = 3b = 3(21) \\ \boxed{e= 63}[/tex]

♨Rage♨

What is the range of the graphed function?
0-5 0-4 Sy < 0
oo sys 4
o {0,1,2,3,4}

Answers

Answer:

Step-by-step explanation:

y equels 4

Find the LCD of the two fractions 1/6 and 1/5

A. 6

B. 5

C. 30

D. 11

Answers

Answer:

C. 30 is the correct answer.

Step-by-step explanation:

Help please

Will mark as brainliest!!!

Answers

Answer:

c

Step-by-step explanation:

3 folders cost $2.91 dollar sign . Which equation would help determine the cost of 2 folders? WRITE THE LETTER IN THE SPACE BELOW.

Answers

Answer:

$1.94

Step-by-step explanation:

Cost of 3 folders = $2.91

We need to find the cost of 2 folders.

First we will find the cost of 1 folder

1 folder = $2.91/3 = $0.97

To find the cost of 2 folders, multiply $0.97 and 2

2 folders = $0.97 × 2

= $1.94

Hence, the cost of 2 olders is $1.94.

If A is a square matrix of order 2, then det(-3A) is *
a. 3 det A
b. -3 det A
c. 9 det A
d. -9 det A
Help please.​

Answers

Answer:

c. 9 det A

Step-by-step explanation:

Given the following data;

Since A is a square matrix of order 2, we know that n = 2

K = 3

For any scalar k;

∣kA∣ = k^{n} ∣A∣

Substituting into the equation;

∣-3A∣ = -3²∣A∣

Simplifying, we have;

∣-3A∣ = 9∣A∣

= 9 detA

Therefore, det (-3A) = 9 detA

In △ABD, DG=40 in.
What is the length of DF?

Enter your answer in the box.

Answers

Answer:

60. GF=20 so add those together

Step-by-step explanation:

Answer:60in

Step-by-step explanation:

What does point B represent on the graph?

John’s Earnings
Hours Worked
Money
1
$7.00
2
$14.00
3
$21.00

On a coordinate plane, a graph titled John's Earnings has hours worked on the x-axis and money on the y-axis. Point A is (1, 7), point B is (2, 14), point C is (3, 21).

John earns $14.00 each hour.
John earns $14.00 for two hours of work.
John earns $7.00 for two hours of work.
John earns $7.00 for four hours o

Answers

Answer:

John earns $14.00 for two hours of work.

Step-by-step explanation:

(x+0.5)^3 Expand the Equation using Pascal’s Triangle and the Binomial Theorem.

Answers

Answer: x^3 + 1.5x^2 + 0.75x + 0.125

Step-by-step explanation:

Use the binomial expansion theorem to find and simplify each term.

At a bakery, Victor makes 20 cupcakes. He puts them

in equal rows with 10 cupcakes in each row. Which

calculation can be used to find the number of rows of

cupcakes Victor makes?


A 20 x 10


B 20/10


C 20-10


D 20+10

Answers

It would be B 20/10
Since she puts 10 in each row

Which  calculation can be used to find the number of rows of

cupcakes Victor makes?you can use b and c

How much simple interest would x dollars earn in 13 months at a rate of r percent?​

Answers

16 im adding this for yes reasons

7+5(x−3)=227, plus, 5, left parenthesis, x, minus, 3, right parenthesis, equals, 22 a true statement?

Answers

Answer:

x = 47

Step-by-step explanation:

Given the equation :

7+5(x−3)=227

Expand the equation :

7 + 5x - 15 = 227

5x = 227 + 15 - 7

5x = 235

x = 235 /5

x = 47

Statement is true at x = 47

Agourmet coffeeshop bought 45 pounds of roasted coffee beans in two weeks. If they bought 20 pounds the second week, how many pounds did they buy the first week?


Please Help

Answers

Answer:

yeeyyesyyyseyas

Step-by-step explanation:

66,722 Cincinnati residents over the age of 25 have a bachelor's degree or higher. What percentage of Cincinnati residents who are over the age of 25 have a bachelor's degree or higher

Answers

Answer:

we are missing some information, so I looked for a similar question and found the attached image:

Cincinnati's total population = 298,957 people

Cincinnati's population over age 25 = 193,638

I added all the people that were up to 24 years old and then subtract that number from 298,957 - 105,319 = 193,638

Percentage of Cincinnati residents over age 25 that have a bachelor's degree or higher = 66,722 / 193,638 = 0.3446 = 34.46%

All of the following are terminating decimals except _____.

Answers

We would have to divide every single one of these fractions to find out if they were terminating decimal. 2/5 = 2divided by 5 = 0.4 as you can see no many other repeating numbers after the decimal. We don't have to do the rest since we now know the answer is 2/5.

Find the slope of each line passing through the given points using the slope formula.
(-3, -10) and (-1, -1) URGENT Please answer

Answers

Slope (m)= y\x= 9/2 = 4.5

your equation for the line is

y=4.5x+3.5

h(x) = 3x2 - 2x + 13
h(3)
[?]

Answers

Answer:

34

Step-by-step explanation:

h(x)=3x^2-2x+13

h(3)=3(3)^2-2(3)+13

h(3)=3(3)(3)-6+13

h(3)=3(9)-6+13

h(3)=27-6+13

h(3)=21+13

h(3)=34

Tina earned $1.38 per day for two days as interest on her $1,000.00 investment. Select all the expressions you could use to find the percent interest she earned in total.

ALSO FREE 100 points

Answers

thx for the free points but i was looking for the answer  

Answer: oooh why thank you

Step-by-step explanation:


Sally sold seashells by the seashore for 3 days for $2.45 per seashell. On the first day, she sold twice as many seashells as the second day, and on the second day, she sold four seashells less than she sold on the third day. If she sold 7 seashells on the third day, how much money did she make on those three days?
seashells less than she sold on the third day. If she sold 7 seashells on the third day, how
much money did she make on those thre

Answers

Step-by-step explanation:

1st day: 6 seashells, 14.7 dollars

2nd day: 3 seashells, 7.35 dollars

3rd day: 7 seashells, 17.15 dollars

All together: 39.2 dollars

day 3 = 7

day 2 = 7 - 4 = 3

day 1 = 3 * 2 = 6

total seas shells = 7 + 3 + 6 = 16

total money = 16 * 2.45 = $39.20

can someone tell me if I’m right or wrong
I got x=5,-5,i,-i on a calculator
But the answer choice has 1

Answers

Answer:

For that particular polynomial your answer would be

x1=-5, x2=5

Answer:

B: [tex]-5, 5, i[/tex]

Step-by-step explanation:

The roots are [tex](x-5)(x+5)(x^{2}+1)[/tex] according to my TI-89 calculator.

Rivas bought a can of paint. He used 3/8 of it to paint a bookshelf. He used 1/4 of it to paint a wagon. He used some of it to paint a birdhouse and has 1/8 of paint left. How much did he use for the birdhouse?

Answers

Answer:

he used 1/8 of paint .....

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