Question

Can someone please help me with this question?

Find Pk+1 for the given Pk.

Answer 1

\[P _{k}=k^2(2k+2)\]

Answer 2

Replace every \(k\) you see with \(k+1\):
\[P_k:~k^2(2k+2)~~\Rightarrow~~P_{k+2}:~(k+1)^2(2(k+1)+2)\]

Answer 3

Then what? I dont understand, I am sorry.

Answer 4

Well, that would be an acceptable answer, though you could simplify it a bit.
\[(k+1)^2(2(k+1)+2)=(k+1)^2(2k+4)\]

Answer 5

Alright, thank you so much. I appreciate your help!