What use is ((a+1)a)/2=b?

Question

The term 'triangular number' is new to me but it describes the resulting value of 'b' concisely.
I think it's a little piece of magic like pythagoras and should be more widely known but I can't think of many practical ways to use it.
There are some good answers here and Muralasa was the first to pin down its significance.

Answer 1

That's the formula for triangular numbers. You can use it to count the number of items in a pyramid shape if you know the number of rows. For example, bowling pins are arranged in a pyramid shape, and there are 4 rows. So, let's make a = 4. Then b = ((4 + 1) * 4) / 2 = 5 * 4 / 2 = 20 / 2 = 10. So, because there are 4 rows of bowling pins and they are arranged in a pyramid shape, there are 10 pins altogether.

Answer 2

It is the formula for the sum of the first 'a' numbers in the number series. 'a' being the number of numbers to be added; and 'b' their sum.

examples to add the first 'a' numbers, we get:
when a is 1 = 1 = (1+1)*1/2 = 1
when a is 2 = 1+2 = (2+1)*2/2 = 3
when a is 10 = 1+2+3+4+5+6+7+8+9+10= (10+1)*10/2=55

So to know the sum of the first 'a' numbers; just use the formula
sum b = ((a+1)a)/2

Answer 3

Imagine "a" is the complex frequency, and "b" is an impulsive forcing function. Your equation has just embodied a second order linear system with a zero at the origin, and a zero at -1. This is a very important result. Forms the basis of many of our modern day industrial achievements. You should seriously consider memorizing that equation, even if it is the last thing you learn.

Answer 4

to work out triangle numbers

Here is 21 examples

1 = ((1+1)*1)/2
3 = ((2+1)*2)/2
6 = ((3+1)*3)/2
10 = ((4+1)*4)/2
15 = ((5+1)*5)/2
21 = ((6+1)*6)/2
28 = ((7+1)*7)/2
36 = ((8+1)*8)/2
45 = ((9+1)*9)/2
55 = ((10+1)*10)/2
66 = ((11+1)*11)/2
78 = ((12+1)*12)/2
91 = ((13+1)*13)/2
105 = ((14+1)*14)/2
120 = ((15+1)*15)/2
136 = ((16+1)*16)/2
153 = ((17+1)*17)/2
171 = ((18+1)*18)/2
190 = ((19+1)*19)/2
210 = ((20+1)*20)/2

48773052894436800000 =((9876543210+1)*9876543210)/2

Answer 5

15

Answer 6

((a+1)a)/2=b
(a^2+a)/2=b
if a=1, then b=1
a=2, b=3
a=3, b=6
a=4, b=10

1,3,6,10 triangular numbers

Answer 7

It could have many uses, mostly in engineering and stress calculations. ((a+1)a)+/2=b so a squared + a divided by 2 equals b therefore a+a=b so a =a/b. confusing enough? lol
Never was that good at math. but i took a shot at it.

Answer 8

a^2+a=2b
a^2+a-2b=0 is a quadratic equation in a

Answer 9

It identifies the series:
1,3,6,10, 15,.....

(triangular numbers)

.....using aa + a = 2b

Answer 10

There is no use for that unless you specify what a specific variable equals or which specific variable to find.