If P(k) = k2 (k + 2)(k – 1) is true, then what is P (k + 1)?

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Solution:

$P(k)=k^2(k+2)(k-1)$

Now, replace $k$ with $(k+1)$ ,

$P(k+1)=(k+1)^2(k+1+2)(k+1-1) \\=(k^2+1+2k)(k+3)(k) \\=k(k+3)(k^2+2k+1)$

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Question ID: mtid-5-stid-8-sqid-3028-qpid-1727