I am looking for an equation that will sum the number of digits of a number i.e. for 4, 1 + 2 +3 + 4 = 10 for 5, 1 +2 +3 + 4 + 5 = 15. I want to replace 4 and 5 with a variable so that any number can be added up to give an answer.
So, you want the sum 1+2+3+...+(n-1)+n?
Here lies the reader who will never open this book. He is forever dead.
Welcome to the forum.
Known as the sum of counting numbers (or triangle numbers) formula, what you want is:
The diagram below shows where it comes from.
If you stack up n then n-1, then n-2 ....... 3, 2, 1 squares it makes a sort of right angled triangle.
Then make the same again but turn this stack up-side-down and slot it into the triangle to make a rectangle.
The rectangle is 'n' high and n+1 wide so its area is n(n+1).
But we've made twice the sum you want, so divide by 2.
Last edited by bob bundy (2013-12-16 09:39:16)