If `(2+x)(2+x^2)(2+x^3)………..(2+x^100)=sum_(r=0)^n k_rx^r, then` n= (A) 2550 (B) 5050 (C) `2^8` (D) none of these

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

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

(x-2)^(100)=sum_(r=0)^(100)a_(r)x^(r), then a_(1)+2a_(2)+......+100a_(100)=

If n is a positive integer then (1+x)^n=^nC_0 x^0+^nC_1 x^1+^nC_2^2+………+^nC_rx^r= sum _(r=0)^n ^nC_rx^r and (1-x)^n= ^nC_0x^0-^nC_1 x^1 +^nC_2-^nC_3x^3+………+(-1)^n ^nC_nx^n=sum_(r=0)^n (-1)^r ^nC_r x^r On the basis of above information answer the following question: If n is a positive integer then 1/((49)^n) - 8/((49)^n)(^(2n)C_1)+8^2/((49)^n)( ^(2n)C_2)- 8^3/((49)^n)(^(2n)c_3)+......+8^(2n)/((49)^n)= (A) -1 (B) 1 (C) (64/49)^n (D) none of these

Let S_n=sum_(r=0)^oo 1/n^r and sum_(n=1)^k (n-1)S_n = 5050 then k= (A) 50 (B) 505 (C) 100 (D) 55

If D_k=|[1,n,n],[2k,n^2+n+2,n^2+n],[2k-1,n^2,n^2+n+2]| and sum_(k=1)^n D_k=48 ,then n equals (a)4 (b) 6 (c) 8 (d) none of these

If (1+x+x^(2))^(n)=sum_(r=0)^(2n)a_(r)x^(r), then a_(1)-2a_(2)+3a_(3)-...-2na_(2n)=

If cos^(3)x sin2x=sum_(r=0)^(n)a_(x)sin(rx),AA x in R then