How can I force Mathematica to simplify sum containing finite geometric sequence?
s=Sum[q^k,{k,0,20}]
(* s=1 + q + q^2 + q^3 + q^4 + q^5 + q^6 + q^7 + q^8 + q^9 + q^10 + q^11 +
q^12 + q^13 + q^14 + q^15 + q^16 + q^17 + q^18 + q^19 + q^20 *)
Simplify[s, q != 1]
(* I get *)
(* 1 + q + q^2 + q^3 + q^4 + q^5 + q^6 + q^7 + q^8 + q^9 + q^10 + q^11 +
q^12 + q^13 + q^14 + q^15 + q^16 + q^17 + q^18 + q^19 + q^20 *)
(* I would like to get *)
(* (q^21 - 1)/(q - 1) *)