If `(1 + x)^n= sum_(r=0)^n C_r x^n and sum_(r=0)^n C_r/(r+1)=k` then the value of k 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 (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+x^2+x^3)^n=sum_(r=0)^(3n)b_r x^r and sum_(r=0)^(3n)b_r=k ,"t h e n"sum_(r=0)^(3n)r b_r is

If (1+x+x^2+x^3)^n=sum_(r=0)^(3n)b_r x^r and sum_(r=0)^(3n)b_r=k ,"t h e n"sum_(r=0)^(3n)r b_r is

If (1+x)^n=sum_(r=0)^n C_rx^r then prove that sum_(r=0)^n (C_r)/((r+1)2^(r+1))=(3^(n+1)-2^(n+1))/((n+1)2^(n+1))

If (1+x+x^(2)+x^(3))^(n)=sum_(r=0)^(3n)b_(r)x^(r) and sum_(r=0)^(3n)b_(r)=k, the n sum_(r=0)^(3n)rb_(r)

If n in N such that is not a multiple of 3 and (1+x+x^(2))^(n) = sum_(r=0)^(2n) a_(r ). X^(r ) , then find the value of sum_(r=0)^(n) (-1)^(r ).a_(r).""^(n)C_(r ) .

If n in N such that is not a multiple of 3 and (1+x+x^(2))^(n) = sum_(r=0)^(2n) a_(r ). X^(r ) , then find the value of sum_(r=0)^(n) (-1)^(r ).a_(r).""^(n)C_(r ) .