Step-by-step explanation:
k has to be replaced by k+1.
so,
4 / ((k+1)(k+1 + 3)) = 4 / ((k+1)(k+4))
I am not sure how far your teacher expects you to go with this.
just in case, I will do also the full multiplications
4 / ((k+1)(k+4)) = 4 / (k² + 4k + k + 4) = 4 / (k² + 5k + 4)
and if you need the factor to go from Pk to Pk+1 :
Pk+1 / Pk = (4/((k+1)(k+4))) / (4/(k(k+3)) =
= (4/((k+1)(k+4))) × (k(k+3))/4 =
= (k(k+3)) / ((k+1)(k+4))
