If `sum_(i=0)^(2n)a_r(x-1)^r =sum_(r=0)^(2n)b_r(x-2)^r and b_r=(-1)^(r-n)` for all `r leq n`, then `a_n=`

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)^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_(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)) .

If a_n=sum_(r=0)^n1/(nC_r), then sum_(r=0)^n r/(nC_r) equals

If sum_(r=1)^(n)cos^(-1)x_(r)=0, then sum_(r=1)^(n)x_(r) equals to