Show that the roots of the equation `(1 + x)^(2n) + (1 - x)^(2n) = 0` are given by `x= +- i tan {(2k-1)pi/(2n)`) where `k=1,2,3,...n.`

Show that the middle term in the expansion (x-1/x)^(2n)i s (1. 3. 5 (2n-1))/n(-2)^n .

Show that the middle term in the expansion (x-1/x)^(2n)i s (1. 3. 5 (2n-1))/n(-2)^n .

If the middle term of (1+x)^ (2n) is (1.3.5….(2n-1)k)/(n!) then k=

If alpha, beta are the roots of the equation x^(2) - 2x + 4 = 0 then for any n in N show that alpha^(n) + beta^(n) = 2^(n+1) cos ((n pi)/3) .

If alpha, beta are the roots of the equation x^(2) - 2x + 4 = 0 then for any n in N show that alpha^(n) + beta^(n) = 2^(n+1) cos ((n pi)/3) .

The number of real roots of the equation 1+a_(1)x+a_(2)x^(2)+………..a_(n)x^(n)=0 , where |x| lt (1)/(3) and |a_(n)| lt 2 , is

The number of real roots of the equation 1+a_(1)x+a_(2)x^(2)+………..a_(n)x^(n)=0 , where |x| lt (1)/(3) and |a_(n)| lt 2 , is

If alpha,beta are the roots of equation , x^(2)-3x+1=0 and , f(n)=alpha^(n)+beta^(n),n in I ,then , f(n+2)=k.f(n)-f(n-2) , where k is , (A) 8 (B) 9 (C) 7 (D) 6

If the middle term in the expansion of (1 + x)^(2n) is (1.3.5…(2n - 1))/(n!) k^(n).x^(n) , the value of k is