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_(1)+a_(2)…..+a_(2n)=3^(n)`

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_(2)+a_(4)+……+a_(2n)=(3^(n)+1)/(2)

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n) , then prove that a_(1)+a_(3)+a_(5)+….+a_(2n-1)=(3^(n)-1)/(2)

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+3x-2x^(2))^(10)=a_(0)+a_(1)x+a_(2)x^(2).+…+a_(20)x^(20) then prove that a_(0)+a_(1)+a_(2)+……+a_(20)=2^(10)

If (1+3x-2x^(2))^(10)=a_(0)+a_(1)x+a_(2)x^(2).+…+a_(20)x^(20) then prove that a_(0)-a_(1)++a_(2)-a_(3)+……+a_(20)=4^(10)

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) then prove that a_0 +a_2 +a_4+……+a_(2n) = (3^n +1)/(2)

If ( 1 + x ) ^(n) = a_(0) + a _(1) x + a_(2) x^(2) + ………. + a_(n)x^(n) , then show that (i) a_(0) - a_(2) + a_(4) - a_(6) + ……… = 2^(n//2) cos . (npi)/4 (ii) a _(1) - a_(3) + a_(5) - a_(7) + …….. = 2^(n//2) sin . (npi)/4

If (1 + x +x^2)^n = a_0 =a_1x + a_2x^2 + ….+a_(2n)x^(2n) then prove that a_1 +a_3 +a_5 + …..a_(2n - 1) = (3^n - 1)/(2)