If `(1 + x +x^2)^n = a_0 +a_1x + a_2x^2 + ….+a_(2n)x^(2n)` then prove that `a_0 +a_2 +a_4+……+a_(2n) = (3^n +1)/(2)`

If (3 + 7x - 9x^2)^n = a_0 +a_1x + a_2 x^2 + ……+a_(2n)x^(2n) prove the a_0 +a_1 +a_2 + ……+a_(2n) = 1

If (3 + 7x - 9x^2)^n = a_0 +a_1x + a_2 x^2 + ……+a_(2n)x^(2n) prove the a_0 + a_2 +a_4 + …….= (1+ (-13)^n)/(2)

If (1 + 3x - 2x^2)^10 = a_0 + a_1x + a_2x^2 +…..+a_20 x^20 thn prove that a_1 +a_3 + a_5 + ……+a_19 = 2^9 - 2^19

If (1+2x +3x^2)^10 = a_0 +a_1x +a_2x^2 + ……+a_20x^20 then a_1 = ?

( 1 + x + x^(2))^(n) = a_(0) + a_(1) x + a_(2) x^(2) + …+ a_(2n) x^(2n) , then a_(0) + a_(1) + a_(2) + a_(3) - a_(4) + … a_(2n) = .

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n) , then prove that a_(0)+a_(3)+a_(6)+a_(9)+……=3^(n-1)

If (1-x+x^2)^n=a_0+a_1x+a_2x^2+ .........+a_(2n)x^(2n),\ find the value of a_0+a_2+a_4+........+a_(2n)dot

If (1+x+x^2)^n=a_0+a_1x+a_2x^2++a_(2n)x_(2n), find the value of a_0+a_6++ ,n in Ndot

If (18x^2+12x+4)^n = a_0 +a_(1x)+ a_(2x)^2 +......+ a_(2n)x^(2n) , prove that a_r= 2^n3^r ( "^(2n)C_r + "^(n)C_1 "^(2n-2)C_r + "^(n)C_2 "^(2n-4)C_r + ....

If (1+x+x^2)^n=a_0+a_1x+a_2x^2++a_(2n)x^(2n), find the value of a_0+a_3+a_6++ ,n in Ndot