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K(k+1)(k+2)÷3

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K(k+1)(k+2)÷3

    • Posted by Ripush Garg 6 years, 7 months ago

    CBSE > Class 11 > Mathematics
    • 1 answers

    Dev Kumar Aidaswani 6 years, 7 months ago

    We first take P (n)=1 Then, P (n)=1 (1+1)(1+2) =1 (2)(3) P (n)=6 Therefore 6is divisible by3 So,P (n)is true for 1 Now let us assume k (k+1)(k+2)=3x Now let p (n)=k+1 So, 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 3 IF 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 3 SIMILARILY THE CASE APPLIED WITH K+1 AND K+2 WE GET IN ALL CASES 3 IS DIVISIBLE THEREFORE K (K+1)(K+2) IS DIVISIBLE BY 3 HENCE PROVED

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