Question

HELP WITH FIRST PRINCIPLES !
1 + 2 + 3 + . . . + n =[n(n + 1)]/2

Prove this result from First principles.

Answer 1

add forwards and backwards, then divide by 2. i assume you mean prove without using induction

Answer 2

1 + 2+ 3+ 4+5+...+(n-1)+n
n+(n-1)+(n-2)+...+ 2 + 1
add to get n + 1 copies of n, so twice your sum is
\[n(n-1)\] making your sum \[\frac{n(n+1)}{2}\]

Answer 3

yes i meant prove without induction .
i dont get the part where you add to get n+1 copies of n .
would you mind further explaning that part to me ? :) thanks

Answer 4

What he means is if u look at each column, they all add up to (n+1) and there are n of these columns so n(n+1).