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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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If jummai is 12years old and Tunde is 8years old and they share 15bananas in the ratio of their ages how many will each have sho
bixtya [17]

Jummai and Tunde will each have 9 and 6 bananas respectively.

For the given ratio case we use the sharing ratio criterion to solve the problem.

Jummai is 12 years old.

Tunde is 8 years old.

Their ages are in ratio of;

                             A = 12 : 8

                             A =  3 : 2

The ratio's sum is 5.

15 bananas total are available for sharing.

Jummai will have x\\ bananas  x = (15 x 3/5) = 9

Tunde will have y bananas  y = (15 x 2/5) = 6

Jummai and Tunde will each have 9 and 6 bananas with them.

To learn more about Ratio click here:

brainly.com/question/13419413

#SPJ4

5 0
1 year ago
By what percent has the rhinoceros weight increased
romanna [79]

let's first off  convert those mixed fractions to improper fractions, then get their difference.

\bf \stackrel{mixed}{1\frac{1}{2}}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}}~\hfill \stackrel{mixed}{2\frac{1}{10}}\implies \cfrac{2\cdot 10+1}{10}\implies \stackrel{improper}{\cfrac{21}{10}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{21}{10}-\cfrac{3}{2}\implies \stackrel{\textit{using the LCD of 10}}{\cfrac{(1)21-(5)3}{10}}\implies \cfrac{21-15}{10}\implies \cfrac{6}{10}\implies \cfrac{3}{5}

now, the original amount, 3/2, if that is the 100%, what is 3/5 off of it in percentage?

\bf \begin{array}{ccll} amount&\%\\ \cline{1-2}\\ \frac{3}{2}&100\\\\ \frac{3}{5}&x \end{array}\implies \cfrac{~~\frac{3}{2}~~}{\frac{3}{5}}=\cfrac{100}{x}\implies \cfrac{3}{2}\cdot \cfrac{5}{3}=\cfrac{100}{x}\implies \cfrac{5}{2}=\cfrac{100}{x} \\\\\\ 5x=200\implies x=\cfrac{200}{5}\implies x=40

4 0
3 years ago
Which of these shapes are quadrilaterals? Choose ALL the correct answers.
kherson [118]

Answer:

The red square, the green rectangle, the pink rhombus, and the green trapezoid.

Step-by-step explanation:

A quadrilateral is a shape that has 4 sides so all you have to do is count how many sides the shape has.

3 0
2 years ago
Graph the line for <br> y+1=−3/5(x−4)<br> on the coordinate plane.
Naddika [18.5K]
Please enclose that -3/5 in parentheses:  <span>y+1= (−3/5)(x−4)
</span>
Let's use the intercept method to graph this line.
First, set x = 0 and find y; this y will be the y-coordinate of the vertical intercept:

y+1= (−3/5)(0−4)  =>  y = -1 + 12/5 = -5/5 + 12/5 = 7/5.  Plot (0, 7/5).

Next, set y = 0 and find x; this will give us the coordinate of the horiz. int.:

0+1= (−3/5)(x−4) => -5/3 = x - 4, or x = 4- 5/3, or  x = 7/3.  Plot (7/3, 0).

Now draw a straight line thru these two points.

6 0
3 years ago
Read 2 more answers
Colin &amp; Brian share a lottery win of £2100 in the ratio 4 : 1. Colin then shares his part between himself, his wife &amp; th
Paraphin [41]

Answer:

His wife gets $336 more than his son.

Step-by-step explanation:

Colin and Brian:

Ratio of 4:1.

So Colin gets \frac{4}{4+1} = \frac{4}{5} of the prize.

\frac{4*2100}{5} = 1680

Colin got $1680. Dividing between himself, his wife and their son:

Ratio of 2:5:3.

So Colin gets \frac{2}{2+3+5} = \frac{2}{10}, his wife gets \frac{5}{2+3+5} = \frac{5}{10} and his son gets \frac{3}{2+3+5} = \frac{3}{10}

Wife:

\frac{5*1680}{10} = 840

His wife got $840.

Son:

\frac{3*1680}{10} = 504

His son got $504.

How much more does his wife get over their son?

840 - 504 = 336

His wife gets $336 more than his son.

8 0
3 years ago
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