Divide `x^(2n)+a^(2^(n-1))x^(2^(n-1))+a^(2^n)` by `x^(2^(n-1))-a^(2^(n-2))x^(2^(n-2))+a^(2^(n-1))`

(x^(2^(n-1))+y^(2^(n-1)))(x^(2^(n-1))-y^(2^(n-1)))=

(x^(2^n)-y^(2^n))/(x^(2^(n-1))+y^(2^(n-1)))=

If A=([x,x],[x,x]) then A^(n)(n in N)= 1) ([2^nx^n,2^nx^n],[2^nx^n,2^nx^n]) 2) ([2^(n-1) x^n,2^(n-1) x^n],[2^(n-1) x^n,2^(n-1) x^n]) 3) I 4) ([2^(n) x^(n-1),2^(n) x^(n-1)],[2^(n) x^(n-1),2^(n) x^(n-1)])

If x_1, x_2, x_3,...... x _(2n) are in A.P , then sum _(r=1)^(2n) (-1)^(r+1) x_r^2 is equal to (a) (n)/((2n-1))(x _(1)^(2) -x _(2n) ^(2)) (b) (2n)/((2n-1))(x _(1)^(2) -x _(2n) ^(2)) (c) (n)/((n-1))(x _(1)^(2) -x _(2n) ^(2)) (d) (n)/((2n+1))(x _(1)^(2) -x _(2n) ^(2))

Find the sum (x+2)^(n-1)+(x+2)^(n-2)(x+1)^+(x+2)^(n-3)(x+1)^2++(x+1)^(n-1) (x+2)^(n-2)-(x+1)^n b. (x+2)^(n-2)-(x+1)^(n-1) c. (x+2)^n-(x+1)^n d. none of these

Find the sum (x+2)^(n-1)+(x+2)^(n-2)(x+1)^(+)(x+2)^(n-3)(x+1)^(2)++(x+1)^(n)(x+2)^(n-2)-(x+1)^(n) b.(x+2)^(n-2)-(x+1)^(n-1) c.(x+2)^(n)-(x+1)^(n) d.none of these

If |[x^(n-1), x^(n+1), x^(n+2)] ,[y^(n-1), y^(n+1), y^(n+2)], [z^(n-1), z^(n+1), z^(n+2)]|= (x-y)(y-z)(z-x)(x^(-1)+y^(-1)+z^(-1)) then n=

16.Prove that (x^(n))/(n)!+(x^(n-1)*a)/((n-1)!1!)+(x^(n-2)*a^(2))/((n-2)!2!)......+(a^(n))/(n!)=((x+a)^(n))/(n!)

Find the sum (x+2)^(n-1)+(x+2)^(n-2)(x+1)^+(x+2)^(n-3)(x+1)^2++(x+1)^(n-1)