Sn=1*2*3+2*3*4+……+n(n+1)(n+2)=(1³+2³+3³+----+n³)+3(1²+2²+3²+---+n²)+2(1+2+3+----+n)=n²(n+1)²/4+n(n+1)(2n+1)/2+n(n+1)=n(n+1)[n(n+1)/4+(2n+1)/2+1)]=n(...