Studying Mathematics Thread

[robvalue]

To prove 1+2+3+...+n=n(n+1)/2

Let S = 1+2+3+...+n

In this case, S is also:
n+n-1+n-2+...+1

If you add both equations of S, you get:

2S=n+1+(n-1+2)+(n-2+3) + ... + n+1

2S = n+1 + n+1 + n+1 + ... + n+1   (n times)

Therefore S = n(n+1)/2

Therefore 1+2+3+...+n = n(n+1)/2

Now for the other two theorems stated in my previous post, how to derive them remains a puzzle to me at this stage. I can prove them via mathematical induction only.

I can show you how if you want