Coins=(1+p t + p^2 t^2+p^3 t^3)(1+n t + n^2 t^2)(1+d t)(1 + q t)(1+ h t)

Collect[Expand[Coins],t]

p=1;n=1;d=1;q=1;h=1;Collect[Expand[Coins],t]

Rico=(x+y)^8

Expand[Rico]

p=1

(1+p t +p^2 t^2 +...+p^8 t^8)

this doesn't seem to work - darn!

Table[p^n t^n,{n,0,8}]

this still didn't work - it thinks p is still = 1

Clear[p,n,d,q,h]

Table[p^n t^n,{n,0,8}]

Sum[p^n t^n,{n,0,8}]

Sum[p^i t^i,{i,0,8}]

Sum[p^i t^i,{i,0,8}]Sum[n^i t^i,{i,0,8}]Sum[d^i t^i,{i,0,8}]Sum[q^i t^i,{i,0,8}]Sum[h^i t^i,{i,0,8}]

Expand[Sum[p^i t^i,{i,0,8}]Sum[n^i t^i,{i,0,8}]Sum[d^i t^i,{i,0,8}]Sum[q^i t^i,{i,0,8}]Sum[h^i t^i,{i,0,8}]]

Expand[(Sum[ t^i,{i,0,8}])^5]

Expand[(Sum[ t^i,{i,0,9}])^5]

Expand[(Sum[ t^i,{i,0,Infinity}])^5]

Wait, this is a mighty curious result - to be continued, in class!

Plot[1/(1-x),{x,-5,5}]

Plot[{1/(1-x),1+x+x^2+x^3+x^4+x^5+x^6},{x,-0,1}]