1+2+3+4...+n = n(n+1)/2

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

-- Por Inducción
if n = 0 then 
   0 = 0·1 /2 = 0; 
   is true;

if p(n) then p(n+1)
  1 + 2 + 3 + ... + n + n+1 = (n+1)(n+2) / 2 ;
  n(n+1)/2 + n+1 = (n+1)(n+2) / 2 ;  -- *2
  n(n+1)  +  2(n+1) = (n+1)(n+2) ;   -- /(n+1)
  n  +  2  = (n+2) 
  is True;

then 1+2+3+4...+n =  n(n+1)/2
  is true;