- #1
Genericcoder
- 131
- 0
Hi guys,
I am noobie in number theory so if something exists better than this equation I did please don't bash me this is my first equation.
Today I was thinking of a way to count all even from 1 to n,so this way I thought about is like this.
Let me first write the equation,then I will explain the logic.
iNumber = ((iNumber + 1) * (iNumber / 2)) - (((iNumber + 1) * (iNumber / 2) - (iNumber / 2)) / 2)
Okay let me explain how I got this logic,so let's pick odd numbers from 1 to 10 and see how they form.
1 = 0 + 1;
3 = 2 + 1;
5 = 4 + 1;
7 = 6 + 1;
9 = 8 + 1;
So here we have 5 ones,so for example if we removed those ones from the a equation that you add 1 to 10 from it will be like this;
Normal numbers which you added 1 to 10 ->
1 + 2 + 2 + 1 + 4 + 4 + 1 + 6 + 6 + 1 + 8 + 8 + 1 + 10 -
1 + 1 + 1 + 1 + 1,so the numbers now become
0 + 2 + 2 + 4 + 4 + 6 + 6 + 8 + 8 + 10 = 50,but that's 2x,so if we got that number and divide by 2 it will be 25,thats how much odds add up,so if we got the total numbers from 1 to 10 and minus 25 we should get the even number we want;
So let's put that in the equation and see if its right;
((11) * (5)) - (((11) * (5) - (5)) / 2) = 55 - 25 = 30;
2 + 4 + 6 + 8 + 10 = 30;
So the equation is right I am sure this has been done by another mathmetician,but its good to think about it the logic of it is great.
I am noobie in number theory so if something exists better than this equation I did please don't bash me this is my first equation.
Today I was thinking of a way to count all even from 1 to n,so this way I thought about is like this.
Let me first write the equation,then I will explain the logic.
iNumber = ((iNumber + 1) * (iNumber / 2)) - (((iNumber + 1) * (iNumber / 2) - (iNumber / 2)) / 2)
Okay let me explain how I got this logic,so let's pick odd numbers from 1 to 10 and see how they form.
1 = 0 + 1;
3 = 2 + 1;
5 = 4 + 1;
7 = 6 + 1;
9 = 8 + 1;
So here we have 5 ones,so for example if we removed those ones from the a equation that you add 1 to 10 from it will be like this;
Normal numbers which you added 1 to 10 ->
1 + 2 + 2 + 1 + 4 + 4 + 1 + 6 + 6 + 1 + 8 + 8 + 1 + 10 -
1 + 1 + 1 + 1 + 1,so the numbers now become
0 + 2 + 2 + 4 + 4 + 6 + 6 + 8 + 8 + 10 = 50,but that's 2x,so if we got that number and divide by 2 it will be 25,thats how much odds add up,so if we got the total numbers from 1 to 10 and minus 25 we should get the even number we want;
So let's put that in the equation and see if its right;
((11) * (5)) - (((11) * (5) - (5)) / 2) = 55 - 25 = 30;
2 + 4 + 6 + 8 + 10 = 30;
So the equation is right I am sure this has been done by another mathmetician,but its good to think about it the logic of it is great.