If S=1(n)+(2n-1)+3(n-2)+...+r(n+1-r)+...+n(1)
and T=1(n-1)+2(n-2)+3(n-3)+...+r(n-r)+...+(n-1)(1) , where n is a positive integer , prove that
S+T=1/6n(n+1)(2n+1)
I can see the pattern , where :
T=1(n-1+1)+2(n-2+1)+3(n-3+1) and so on but it doesn't lead me anywhere further .
Thanks .