Let `n` be a positive integer and `(1+x+x^2)^n=a_0+a_1x++a^(2n)x^(2n)dot` Show that `a0 2-a1 2+a2 2++a2n2=a_ndot`

Let n be a positive integer and (1+x+x^2)^n=a_0+a_1x++a^(2n)x^(2n)dot Show that a_0^2-a_1^ 2+a_2^ 2++'a_2n' x^2=a_ndot

Let n be a positive integer and (1+x+x^2)^n=a_0+a_1x+ . . . . +a_(2n)x^(2n)dot Show that a_(02) -a_(12)+a_(22)+. . . +a _(2n2)=a_n

Let n be a positive integer such that (1+x+x^2)^n=a_0+a_1x+a_2x^2+…….+a_(2n)x^(2n) then sum_(r=0)^(2n) a_r is

If (1 -x + x^2)^n = a_0 +a_1x + a_2x^2+….+a_(2n)x^(2n) then a_0 + a_2 +a_4 + …….+a_(2n) =

Let n be a positive integer, such that (1 + x + x^2)^n=a_0 +a_1x+ a_2 x^2+a_3 x^3+......a_(2n) x^(2n), Answer the following question: The value of a when (0 leq r leq n) is (A) a_(2n-r) (B) a_(n-r) (C) a_(2n) (D) n. a_(2n-1)

If (1 + x +x^2)^n = a_0 +a_1x + a_2x^2 + ….+a_(2n)x^(2n) then prove that a_0 +a_1 +a_2 + ……a_(2n) = 3^n

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

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

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