Applying this formula is easy. For example, for n=10 we get
1+2+3+4+5+6+7+8+9+10=10(10+1)/2=5(11)=55 and for n=257 we get
1+2+3+...+256+257=257(258)/2=257(129)=33,153.
While there are many simple proofs of this formula, this is the usual "proof by picture." Do you see it?