Fun Identity

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

both sides * α
α + 2α + 3α +...+ nα = nα(nα+1)/2

both sides * sin
 sin α + sin2α +...+ sin nα = sin nα.sin (nα+1)/2

(Discovered by Hua Luogeng )

http://en.wikipedia.org/wiki/Hua_Luogeng