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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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Cual es la diferencia entre divisor y divisible
Anna [14]
La diferencia entre divisor y divisible es que los números compuestos (número que posee más de dos divisores) son los divisores y los números divisible son los números enteros como el 10,15,20,25 y 30.

espero que esto ayude
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What’s the mean of these numbers: 7, 14, 15, 9, 11, 14, 11, 10, and 17
harkovskaia [24]

Answer:

12

Step-by-step explanation:

Mean is the average of all the numbers. Add up all the numbers then divide by how many you have.

7 0
3 years ago
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Solve for x : x/-9=3
USPshnik [31]

Answer:

x=-27

Step-by-step explanation:

x/-9=3

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7 0
3 years ago
Which function represents a translation of the parent cubic function 8 units to the left? h(x) = x3 + 8 h(x) = x3 – 8 h(x) = (x
Ksju [112]

Using the definition of the Vertical shifts of graphs of the function :

"Suppose c>0,

To graph y=f(x)+c, shift the graph of y=f(x) upward c units.

To graph y=f(x)-c, shift the graph of y=f(x) downward c units"

Again we recall the definition of Horizontal shifts of graphs:

" suppose c>0,

the graph y=f(x-c), shift the graph of y=f(x) to the right by c units

the graph y=f(x+c), shift the graph of y=f(x) to the left by c units. "

consider f(x)=x^3 is the parent function.

h(x)=x^3+8 shifts the graph f(x)=x^3 upward by 8 units

h(x)=x^3-8 shifts the graph f(x)=x^3downward by 8 units

h(x)=(x+8)^3 shifts the graph f(x)=x^3 left by 8 units

h(x)=(x-8)^3 shifts the graph f(x)=x^3 right by 8 units.

7 0
3 years ago
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What is the perimeter of triangle ABC? Round each step to the nearest tenth. Please help me
Ad libitum [116K]

I would use the pythagorean theorem to find the lengths of each side. a² + b² = c².

Side AB is one we're looking for. If you make other right triangle with that same side you can see that one length is 4 and the other is 3. So, 4² + 3² = c² → 25 = c² → 5 = c. Side AB is length 5.

Side AC is another. Do the same with that side and you get that one length is 4 and the other is 3. (This is the same one as above) so side AC is length 5.

Side BC is the last one. One of the lengths is 1 and the other is 1 → 1² + 1² = c² → 2 = c² → 1.414213562 = c so side BC is approximately length 1.41.

Add each length up and you get a perimeter of roughly 11.4

8 0
3 years ago
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