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Prove by PMI :- n(n+1)(n+2)(n+3) is …

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Prove by PMI :- n(n+1)(n+2)(n+3) is multiple of 24

    • Posted by Naman Mathur 6 years, 10 months ago

    CBSE > Class 11 > Mathematics
    • 1 answers

    Krittika Kar 5 years, 9 months ago

    For n=1 1(1+1)(1+2)(1+3)=1(2)(3)(4)=24 For P(1) it is true. Let us assumes that it is true for n=k Now, P(k)=k(k+1)(k+2)(k+3)=24x (k+1)(k+2)(k+3)=24x/k.....(1) Now for P(k+1)=(k+1)(k+2)(k+3)(k+4) =24[x(k+4)/k] Therefore, it is true for n=k+1 Thus by PMI, it is true for all n belongs to N

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