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Scilla [17]
2 years ago
8

Please help to find an explicit formula for calculating the sum Mn

Mathematics
1 answer:
defon2 years ago
8 0

The explicit formula for calculating the sum is

S_N=\frac{n(n-1)}{2} \cdot\frac{n(n+1)}{2}

The sum of the nth term of a sequence is expressed as;

S_n=\frac{n}{2}(2a+(n-1)d)

a is the first term

d is the common difference

n is the number of terms

For the sequence  0 + 1 + 2 + 3  +...

S_n=\frac{n}{2}(2(0)+(n-1)1)\\S_n= \frac{n}{2}(n-1)\\S_n= \frac{n(n-1)}{2}

Similarly for the sequence:

1 + 2+ 3 + 4+...

S_n=\frac{n}{2}(2(1)+(n-1)1)\\S_n= \frac{n}{2}(2+n-1)\\S_n= \frac{n(n+1)}{2}

Taking the product of the sum to get the explicit formula for calculating the sum

S_N=\frac{n(n-1)}{2} \cdot\frac{n(n+1)}{2}

Learn more here: brainly.com/question/24547297

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Shelton earns and hourly wage at a grocery store. The following expression represents Shelton's take home pay after taxes, socia
zalisa [80]

If x represents the number of hours Shelton worked, then the expression 10.25x shows how much Shelton is paid for these x hours ($10.25 for an hour).

After taxes, social security, and his health care plan were deducted he earned

10.25x - 0.21(10.25x).

This means that taxes, social security, and his health care plan form 21% (0.21 as decimal) from 10.25x.

Answer: 21%


6 0
3 years ago
Help me find the volume please
Elena L [17]

Answer:

<h2>V = 605 in³</h2>

Step-by-step explanation:

The formula of a volume of a pyramid:

V=\dfrac{1}{3}BH

B - area of a base

H - height

We have the square in the base with side length a = 11 in.

Area of a base:

B=11^2=121\ in^2

Calculate the volume:

V=\dfrac{1}{3\!\!\!\!\diagup_1}(121)(15\!\!\!\!\!\diagup^5)=(1)(121)(5)=605\ in^3

3 0
3 years ago
Can someone give me the answers plz:)
Alborosie

Remark

There is no short way to do this problem and no obvious way to get the answer other that to solve each part.  

Solve

A

\dfrac{x + 1.6}{2} =\text{x + 0.1}                    Multiply by 2

x + 1.6 = 2(x + 0.1)                                         Remove the brackets

x + 1.6 = 2x + 0.1*2                                        

x + 1.6 = 2x + 0.2                                          Subtract x from both sides

1.6 = x + 0.2                                                  Subtract 0.2 from both sides  

1.6 - 0.2 = x                        

1.4 = x

Circle A

B

Subtract 2x from both sides.

3x - 2x = 1.4

Circle B

C

Remove the brackets.

4x + 6 = 2x - 6           Add 6 to both sides

4x + 12 = 2x               Subtract 4x from both sides.

12 = -2x                      Divide by - 2

12/-2 = x

x = - 6                         Don't circle C

D

I'm going to be very scant in my solution of this. You can fill in the steps.

3x = 4.2

x = 4.2/3

x = 1.4

Circle D

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