If `sum_(r=0)^(2n)a_r(x-2)^r=sum_(r=0)^(2n)b_r(x-3)^ra n da_k=1` for all `kgeqn ,` then show that `b_n=^(2n+1)C_(n+1)` .

If sum_(r=0)^(2n)a_r(x-2)^r=sum_(r=0)^(2n)b_r(x-3)^r and a_k=1 for all kgeqn , then show that b_n=^(2n+1)C_(n+1) .

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 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 ge n then show that b_(n ) =""^((2n+1)) C_((n+1)) .

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)=

If sum_(r=0)^(2n)a_(r)(x-100)^(r)=sum_(r=0)^(2n)br(x-101)^(r) and a_(k)=(2^(k))/(kC_(n))AA k>=n then b_(-) n equals ( A )2^(n)(2^(n+1)-1)(B)2^(n)(2^(n)-1)(C)2^(n)(2^(n)+1)(D)2^(n+1)(2^(n)-1)

If (1-x^2)^n=sum_(r=0)^na_rx^r(1-x)^(2n-r) , then a_r is equal to