Question

Given that P(n) : 6 is a factor of n
3
+ 5n, write P(1), P(2), P(k) and P(k+1) where k is
a natural number.

Answer 1

Step-by-step explanation:

P(1)= n^3+5n

=(1)^3+5×1

=6.

P(2)= (2)^3+5×2

=18.

P(k)= k^3+5k.

P(k+1)= (k+1)^3+5(k+1)

= k^3+3k^2+3k+1+5k+1

=k^3+3k^2+8k+6.