Please show how are they equal?

The gross return over the most recent k periods is the the product of the single period gross returns (from time t - k to time t) P Pt-k1 1Rk Pt-k 1+R,(&)--60 () 2) - OLE) = Pt-k However, adjusting for dividends. if a dividend D is paid prior to time t,then the gross return at time t is defined as Pt+D 1+ Rt Pt-1 Here is what I don't understand: Multiple period gross returns are products of single period gross returns so that: Pt+D P-1+D+-1 Pt_k+1+Pt+k+1 1+R4(k)=( P-1 Pt-2 ') (P.. D) PL_k+1) Pt-k Pt + Dt For the last formula(with dividends) 1+R4(k) + 1 as far as I can see, so what is it then? Pt k