if (1+x+x^2)= a0+a1x+a2x^2+a3x^3+........+a2nx^2n then show that

a0+a3+a6+......= 3^(n-1)

• Put x=1,w and w^2 to get terms
  3^n=a0+a1+a2.....+an , ...(1)
  (1+w+w^2)^n=0=a0+a1w+a2w^2+..........anw^n ....(2),
  And (1+w^2+w^4)=0=a0+a1w^2+a2w......+anw^2n...(3)
  
  Now add (1),(2)and (3) to get a0+a1+a2+a3+.....an=3^(n-1)
  
  
  
• 8 years agoHelpfull: Yes(0) No(1)