OK, note that the part in blue
below is just P(k).
What you need to do is expand the right hand side
of both P(k) and of P(k+1). Then, you can subtract Σj=1k
from the left side of the above, and you can also subtract (1/4)x2
from the right side of the above (since those two quantities are equal
What you will be left with is:
which is an identity.
edit: fixed an omission