[" 2.If "sum_(r=0)^(n){a_(r)(x-alpha+2)^(r)-b_(r)(alpha-x-1)^(r)}=0" ,then prove "],[" that "b_(n)-(-1)^(n)a_(n)=0]

If sum_(r=0)^(n){a_(r)(x-alpha+2)^(r)-b_(r)(alpha-x-1)^(r)}=0 , then (a) b_(n) = 1+a_(n) (b) b_(n) = (-1)^(n)xxa_(n) (c) b_(n) = (-1)^(n-1) xxa_(n) (d) b_(n) + 1 = a_(n)

sum_(i=0i0)^(2n)a_(r)(x-1)^(r)=sum_(r=0)^(2n)b_(r)(x-2)^(r) and b_(r)=(-1)^(r-n) for all r<=n, then a_(n)=

sum_(r=0)^(2n)a_(r)(x-2)^(r)=sum_(r=0)^(2n)b_(r)(x-3)^(r) and a_(k)=1 for all k>=n, then show that b_(n)=2n+1C_(n+1)

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of

If (1+x+x^(2))^(n)=sum_(r=0)^(2n)a_(r)x^(r), then prove that a_(r)=a_(2n-r)

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of sum_(r=0)^(n)a_(r) is

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of sum_(r=0)^(n)a_(r) is

If (1-x^(2))^(n)=sum_(r=0)^(n)a_(r)x^(r)(1-x)^(2n-r), then a_(r) is equal to ^(n)C_(r) b.^(n)C_(r)3^(r) c.^(2n)C_(r) d.^(n)C_(r)2^(r)

If (1+2x+x^(2))^(n) = sum_(r=0)^(2n)a_(r)x^(r) , then a_(r) =