How I derived the Gaussian summation formula

[Jesus_ist_König]

I wanted to try yesterday at 12 am how to do it and I did it. Here is what I did.
The normie way is like adding the numbers from 1 to 100 and seeing what comes out. This is too difficult so I made it simpler.

Lets just make an example with tinier numbers.
1 to 5.
1+2+3+4+5

lets look at the pattern
1+5 = 6
2+4 = 6
3 = 3

n in this case is 5
so
n = 5

the six then is

6 = n+1 = 5+1​

getting back to this

Spoiler

lets look at the pattern
1+5 = 6
2+4 = 6
3 = 3

we have 2 times the (n+1) and one time the 3
so lets write it as
2*(n+1)+3

but still there is the 3 that is distracting us. Lets replace it.
3 = 0,5*(n+1)

in total this is: 2*(n+1)+0,5*(n+1) = 2,5*(n+1)

the marked thing in black is our solution so lets make a chart.
on the left side we have n and on the right side we have the formula

​

n​	Formula​
0​	0*(n+1)​
1​	0,5*(n+1)​
2​	1*(n+1)​
3​	1,5*(n+1)​
4​	2*(n+1) ​

So on and so on. Aka what we did with replacing the number 3 in the formula for n =5 in the example from above, we now did with every number in that collumn.
Now any retard can see the pattern but lets say not.

So for every n that we go up the multiplying number or what the fuck its called goes up by 0,5
I.e. we have 0,5*x
so at 4 we get 4*0,5 which is 2.

In this case we can say that the formula is just
0,5x*(n+1)
but since
x = n
we just have to replace it with n and we get

0,5n*(n+1)

this is our formula and this is the answer!

There are many different versions out there to derive it but this one -which I obviously did- was the most easy one.

Its crazy that Gauß did all this shit whilst being 10 years old


@Niebvll

 

[Jesus_ist_König]

My english is so fucking shit

 

[Jesus_ist_König]

@sonic55555 @yyk117

 

[Jesus_ist_König]

bro lies mal durch @armemann

 

[sha]

bookmarking to revisit when im competent enough to understand

 

[armemann]

bro lies mal durch @armemann

Gauss war schon goated

 

[Jesus_ist_König]

bookmarking to revisit when im competent enough to understand

Bro read it now, I made it super easy to understand pls read

 

[Jesus_ist_König]

Gauss war schon goated

Hast du es gelesen?

 

[yyk117]

fire, the equation i always use is the n/2(2a + (n-1)d) one. i never knew this equation

 

[Jesus_ist_König]

fire, the equation i always use is the n/2(2a + (n-1)d) one. i never knew this equation

what do the parameters a and d stand for???
and u r using that for the gauß equation?

 

[armemann]

Hast du es gelesen?

Ja

 

[Jesus_ist_König]

Ja

hast du es verstanden?

 

[armemann]

Das schönste Pattern is mMn Fibonacci oder Mandelbrot

 

[sha]

Bro read it now, I made it super easy to understand pls read

read it but still too advanced for me im in america i gave up in this propagandized goyim school

 

[Jesus_ist_König]

Das schönste Pattern is mMn Fibonacci oder Mandelbrot

Kenn ich nicht

 

[Jesus_ist_König]

read it but still too advanced for me im in america i gave up in this propagandized goyim school

hm

 

[yyk117]

what do the parameters a and d stand for???
and u r using that for the gauß equation?

the sum of an arithmetic sequence formula i was taught is:

a is the first term and d is the common difference
i never knew about the gauß equation

 

[armemann]

hast du es verstanden?

kenne die gaußsche formel aber fand die Erklärung bisl mid

 

[Jesus_ist_König]

the sum of an arithmetic sequence formula i was taught is:

View attachment 5151127
a is the first term and d is the common difference
i never knew about the gauß equation

Never heard about that I will try to get to the formula on my own know this is fun

 

[Niebvll]

Water

 

[Jesus_ist_König]

the sum of an arithmetic sequence formula i was taught is:

View attachment 5151127
a is the first term and d is the common difference
i never knew about the gauß equation

Hmmm okay im finished now. Weird

For calculating the sum of an arithmetic series with always starting at 0 i have:
0,5n*(n+1)*d

Then i wanted to do it with the a. I.e. if a =3 and n =5 then the addition should go from 3 to 5 and leave out everything b4 and after.

I tried to find a fancy way but couldnt. I only got
0,5d*(n²-a²+n-a)


imma ask chatgpt what i did wrong

 

[Jesus_ist_König]

@yyk117 I understood it. In ur formula the a is the real number of the start. For example you want addition to begin at the fourth number. Instead of writing a = 4 (which is what you have to do in my formula) you need to write the actual number that is in fourth position, which could be 47 or 22 or whatever. My a describes the position of the number an urs describes the value of the number.

 

[yyk117]

@yyk117 I understood it. In ur formula the a is the real number of the start. For example you want addition to begin at the fourth number. Instead of writing a = 4 (which is what you have to do in my formula) you need to write the actual number that is in fourth position, which could be 47 or 22 or whatever. My a describes the position of the number an urs describes the value of the number.

ahh yeah i should of specified that, a is n = 1 in the formula i sent.

 

[Jesus_ist_König]

ahh yeah i should of specified that, a is n = 1 in the formula i sent.

I hate that formula its shit i dont like it i like mine more