



 
First off, that last coefficient should be a_40. terms; your expanded expression will have the form $a_0 + a_1x + ... a_{40}x^{40}.$ Look at the more general sums of even and odd coefficients 1 (E(0) = 1, O(0)=0) You should be able to find a conjecture easily (look at E(n)+O(n) if you're stuck) Prove it by induction: assume it true for (E(n),O(n)) and use Good Hunting!  


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