Answer to Question #190212 in Discrete Mathematics for Romnick Lucas

Question

If P(k) = k2

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

Answer 1

Solution:

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

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

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