Question 601352
2+4+6+...+2n = n(n+1). You can prove it by induction. Or you can use the "Gauss-style" method of adding that expression to itself, i.e.


S = 2 + 4 + 6 +...+ 2n
S = 2n+ ...       + 2
----------------------
2S = (2n+2) + (2n+2) + ... + (2n+2) = (2n+2)(n)


S = n(n+1)