kk! = (k+1)! - k!. This identity converts factorial sums into telescoping form. sum(kk!, k=1 to n) = (n+1)! - 1. Similarly: (k+1)*k! = (k+1)!, and $\frac{k}{k+1}$! = 1/k! - $\frac{1}{k+1}$!. These factorial identities are essential for evaluating sums involving factorials in JEE.