Random.org has picked Dooglius as the winner of MMM #27. Congratulations, Dooglius!
The answer to the problem is 1/(w^3-w^2-w+1), or 1/((1-w^2)(1-w))
Tanaeem M Moosa had a very clever demonstration. Check this out:
s=1 + (w+w^2) + (w^2+w^3+w^4) + (w^3 + w^4 + w^5+ w^6) + (w^4 + w^5+ w^6 + w^7 + w^8) + ...
w*s= (w) + (w^2+w^3)+ (w^3+w^4+w^5)+ (w^4+w^5+w^6+w^7)+...
or, s(1-w) = 1/(1-w^2)
Blinkdagger will have their next contest on Monday so check it out there!