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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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Does each function describe exponential growth or decay?
Aleksandr [31]
<h3>Answer: Only first two are exponential growth function and last three functions are exponential decay functions.</h3>

Step-by-step explanation: We need to describe exponential growth or decay for the given functions.

The standard exponential function equation is

y=a(b)^x.

Where a is the initial value and b is the growth factor.

Note: If value of b > 1, it would be an exponential growth and if b < 1, it would be an exponential decay.

Let us check them one by one.

y=(1.008^{1/12}})^{12t} => y=(1.008^})^{1/12\times{12t} }

=> y= (1.008)^t.

Value of b is 1.008 > 1, therefor it's an exponential growth function.

y=250(1+0.004)^t, also have b>1 therefor it's an exponential growth function.

All other functions has b values less than 1, therefore only first two are exponential growth function and last three functions are exponential decay functions.



5 0
3 years ago
The point (-4,1) is rotated 180 degrees counterclockwise using center (-3,0). What are the coordinates of the image?
IrinaVladis [17]
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4 0
2 years ago
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PLEASE HELP NOW!! If K is the set of all letters in the word “equation”, and L is the set of all letters of the word “inequality
satela [25.4K]

Answer:

e,q,u,a,t,i,n & EQUATIONYL

Step-by-step explanation:

K∩L:

First write both the words, equation and inequality down.

E Q U A T I O N

I N E Q U A L I T Y

You can see EQUATIN repeats in both of the words.

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This time just write down all the letters EXCEPT the ones that repeat. EQUATIONYL

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2 years ago
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4 0
3 years ago
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A plane flew for 2 hours at 467 mph (miles per hour) and 5 hours at 536. How far did the plane fly in miles
Archy [21]

Answer:

3614 miles

Step-by-step explanation:

Given data

A plane flew for 2 hours at 467 mph

Let us find the distance covered

Speed= distance/time

Distance= speed*time

Distance= 467*2

Distance=934 miles

5 hours at 536

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Distance= speed*time

Distance= 536*5

Distance=2680 miles

Total distance

=2680+934

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3 0
3 years ago
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