Question

cmr k thuộc N sao ta luôn có

k.(k+1)(k+2)-(k-1).k.(k+1)=3.k.(k+1)

 

Answer 1

Có : VT = k.(k+1).[k+2-(k-1)]

             = k.(k+1).3

             = VP

=> ĐPCM

Tk mk nha

Answer 2

ta có :

\(k\left(k+1\right)\left(k+2\right)-\left(k-1\right)k\left(k+1\right)\)

\(=k\left(k+1\right)\left[\left(k+2\right)-\left(k-1\right)\right]\)

\(=k\left(k+1\right)\left[k+2-k+1\right]\)

\(=k\left(k+1\right)\left[\left(k-k\right)+\left(2+1\right)\right]\)

\(=k\left(k+1\right).3\) (đpcm)