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kaheart [24]
2 years ago
5

Can anyone explain how to do mathematical induction. The question is below. Brainliest awarded for the right answer. Thanks.

Mathematics
1 answer:
igomit [66]2 years ago
3 0

The sum of the triangular numbers is \frac{n(n+1)(n+2)}{6}

According to the question, the series of triangular numbers is given as in the form of the number of dots constituting the equilateral triangles i.e.
1, 3, 6, 10, 15 . . . . .n

<h3>what is triangular numbers?</h3>

triangular number are the sequence and series of the numbers and each number represents and constitute in visualization of  series of  equilateral triangle.

given series in the figure
1, 3, 6, 10, 15, . . . . . .  ., n
each number represents the number of dots containing in triangle
now the series can be given by
S = \frac{n(n+1)}{2}  for n = 1, 2, 3, 4,. . . . .n
now , according to the question the sum of the series can be given as
⇒  ∑S
⇒   ∑\frac{n^2+n}{2}
⇒  \frac{1}{2}[\sum n^2+\sum n]\\\frac{1}{2}[\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2}] \\\frac{n(n+1)}{4}[\frac{(2n+1)}{3}+1] \\\frac{n(n+1)}{4}[\frac{(2n+1+3)}{3}] \\\frac{n(n+1)}{4}[\frac{(2n+4)}{3}] \\\frac{n(n+1)}{4}2[\frac{(n+2)}{3}]\\\frac{n(n+1)(n+2)}{6}

Thus, the sum of the triangular number is given by \frac{n(n+1)(n+2)}{6}

Learn more about triangular numbers here:
brainly.com/question/1417765

#SPJ1

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PLSSS HURRY ILL GIVE YOU A BRAINLYEST
8090 [49]

Answer:

36 inches

Step-by-step explanation:

lets think of it as a ratio,

80:w

20:9

so we want 20 to get to 80

and 9 to get to w right?

so if we just move the smaller rectangle to the corner, then 20*4=80 right?

and if we do that, we do it to 9 as well, 9*4=36

w=36

6 0
2 years ago
19) A six-sided die is rolled six times. What is
aleksley [76]

Answer:

D

Step-by-step explanation:

Probability that the die will show an even number

in one rolling is 3/6=0,5 = p

We have formula for repeating rolling

n!/(r!(n-r)!) p^r (1-p)^(n-r)

n = how many times we repeat rolling = 6

r = how many times we want something to happen

(show an even number exactly two times) = 2

15 *(0,5)^2 *(0,5)^4 = 0,234375

4 0
2 years ago
A _____ is a section on a number line where few to no data points fall.
SVETLANKA909090 [29]
<span>The geometric term described as an infinite set of points that has length but not width is called a line. It has a negligible with and depth. In geometry, a line located in the plane is defined as the set of points whose coordinates satisfy a given linear equation. </span>
8 0
3 years ago
Find an equation to the line perpendicular to 4x + 36y =80 an goes through the point (3,6) write answer in form y= Mx+b
Veronika [31]

Answer:

\textbf{y = 9x + 21 }\\

Step-by-step explanation:

\textup{Given equation is: $4x + 36y = 80  $}\\\textup{This can be written in the form of $y = mx + a$ as follows}\\$ 36y = -4x + 80 $\\$ \implies y = \frac{80}{36} - \frac{4}{36}x $\\$ \implies y = \frac{-1}{9}x + \frac{20}{9} $\\\textup{This means that the slope of this line is $m = \frac{-1}{9}$}\\

\textup{Then the slope of the line perpendicular to this line would be \textbf{negative reciprocal of m}.}\\$i.e.,$ \textup{Slope of the perpendicular line would be $m_1 = \frac{-1}{\frac{-1}{9}}$}\\$\implies m_1 = 9$\\

\textup{The perpendicular line passes through the point $(3,6)$}\\\textup{Using the \textbf{point-slope formula}, we get:}\\

$$ y - y_1 = m(x - x_1) $$$ \implies y - 6 = 9(x - 3) $\\\textup{After solving this reduces to $y = 9x + 21$ }

8 0
3 years ago
u can look this up here on brainly for an answer source if you want but do the one that has the greatest points... its on google
Alla [95]

Answer:

First one is 41

Second one is 87

Step-by-step explanation:

Make the shaded part as a trapezoid which is (3+6)*10/2 you just have to get rid of 2*2. So you get 41 as the answer.

The unshaded part will be 16*8 then subtracts the shaded part which is 41.  Then you get the answer 87.

6 0
3 years ago
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