`sum_(r=0)^300 a_r x^r=(1+x+x^2+x^3)^100`, If `a=sum_(r=0)^300 a_r`, then `sum_(r=0)^300 ra_r`

sum_(r=0)^(300)a_rx^r=(1+x+x^2+x^3)^(100) . If a=sum_(r=0)^(300)a_r , then sum_(r=0)^(300)ra_r is equal to

sum_(r=0)^(300)a_r x^r=(1+x+x^2+x^3)^(100)dot If a=sum_(r=0)^(300)a_r ,t h e nsum_(r=0)^(300)r a_r is equal to 300 a b. 100 a c. 150 a d. 75 a

If (1+x^(2))^(n) =sum_(r=0)^(n) a_(r)x^(r )= (1+x+x^(2)+x^(3))^(100) . If a = sum_(r=0)^(300)a_(r) , then sum_(r=0)^(300) ra_(r) is

If (1+x+x^2+x^3)^n=sum_(r=0)^300 b_rx^r and k=sum _(r=0)^300 b_r=k, then sum_(r=0)^300 r. b_r, is (A) 50.4^100 (B) 150.4^100 (C) 300.4^100 (D) none of these

Let (1 + x + x^(2))^(100)=sum_(r=0)^(200)a_(r)x^(r) and a=sum_(r=0)^(200)a_(r) , then value of sum_(r=1)^(200)(ra_(r))/(25a) is

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

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

If (1-x-x^(2))^(20)=sum_(r=0)^(40)a_(r).x^(r), then

Let (1+x)^(10) = sum_(r=0)^(10) c_(r) x^ (r ) and (1+x)^(7) = sum_(r=0)^(7) d_(r) x^(r ) . If P= sum_(r=0)^(5) c_(2r) and Q= sum_(r=0)^(3) d_(2r+1), then (P)/(Q) is equal to

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)