If 1+x+x2+x3n=a0+a1x+a2x2+a3x3+…+a3nx3n, then the value of  a0+a4+a8+a12+… is 

If 1+x+x2+x3n=a0+a1x+a2x2+a3x3++a3nx3n, then the value of  a0+a4+a8+a12+ is 

  1. A

    -1

  2. B

    0

  3. C

    4n1

  4. D

    n

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    Solution:

    we have 

     a0+a1x+a2x2+a3x3++a3nx3n=1+x+x2+x3na0+a2x2+a4x4++a1x+a3x3+=1+x+x2+x3n

    Putting x = 1, -1, i and -i respectively, we get

    a0+a2+a4++a1+a3+a5+.=4na0+a2+a4+a1+a3+a5+.=0a0a2+a4a6++ia1a3+a5+.=0a0a2+a4a6+ia1a3+a5+.=0

    Adding (i) and (ii), we get 

    2a0+a2+a4+=4n

    Adding (iii) and (iv), we get

    2a0a2+a4a6+..=0 

    Adding (v) and (vi), we get 

    4a0+a4+a8+.=4na0+a4+a8+.=4n1

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