6th Learning essay of probability

Today I've learned an amazing method of calculating from 1 to N, though I've known that equation N(N+1)/2 for a long time, but I think I don' t really understand where it comes from until today.

Arrange 2 string numbers below

1 + 2 + 3 + 4 + 5 + ...................................N

N+(N-1)+(N-2)+(N-3)+(N-4)+....................1

Then add every single 2 numbers together, every 2 numbers combined will be N+1, then we have N numbers, so N(N+1), because we add them twice, there are 2 string of number from 1.........N, so we divide it by 2, then the equation come out as 

N(N+1)/2 

Awesome

then mathematical induction, 1 + 2 + 3 + 4 + 5 + 6 +..........................N+ N+1

it will be like 

N(N+1)/2 + (N+1) 

= (N+1)(N/2+1)

=(N+1)(N+2)/2

Awesome again, the feel of learning something new is always great, keep going Wallace Tiger : )