$T= (-1)^k .k .\frac{1}{(n+1)(n+2)}. C^{k+2}_{n+2}$Đặt $A=k. C^{k+2}_{n+2} = (k+2).C^{k+2}_{n+2} - 2.C^{k+2}_{n+2}$
Đặt $C = (k+2) . C^{k+2}_{n+2} = (n+2). C^{k+1}_{n+1}$
Đấy xong thay vào T ta có : $T= \frac{1}{(n+1)(n+2)} . ( (-1)^k. (n+2).C^{k+1}_{n+1}-2.(-1)^k.C^{k+2}_{n+2})$