[" 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>=],[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 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 k ge n 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)^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)^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)^ra n da_k=1 for all kgeqn , 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 (1+2x+x^(2))^(n) = sum_(r=0)^(2n)a_(r)x^(r) , then a_(r) =

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

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