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| 1. |
K(k+1)(k+2)÷3 |
| Answer» We first take P (n)=1 Then,P (n)=1 (1+1)(1+2)=1 (2)(3)P (n)=6Therefore 6is divisible by3 So,P (n)is true for 1Now let us assume k (k+1)(k+2)=3xNow let p (n)=k+1So,K+1 (K+2)(K+3)SO IF K(K+1)(K+2) IS DIVISIBLE BY 3 SO EITHER ONE OF THEM IS DIVISIBLE BY 3IF K IS MULTIPLE OF 3 SO IN K+1 (K+2)(K+3)K+3 IS MULTIPLE OF 3 SO THE ABOVE NO. IS DIVISIBLE BY 3SIMILARILY THE CASE APPLIED WITH K+1 AND K+2WE GET IN ALL CASES 3 IS DIVISIBLE THEREFORE K (K+1)(K+2) IS DIVISIBLE BY 3HENCE PROVED | |