i=1;
sum=0;
while (i<=N) {
  sum = sum + i;
  i++;
}

Then, we can systematically translate this into Assembler: 

     mov ax,1 ; i = 1 
     mov i,ax
     mov ax,0 ; sum = 0
     mov sum,ax
loop1:
     mov ax,i
     cmp ax,n 
     jg loop1e  ;  while i <= n
     mov  ax,sum  ; sum = sum + i
     add  ax,i
     mov  sum,ax
     mov ax,i  ; i = i + 1
     inc ax
     mov i,ax
     jmp  loop1
loop1e: