If `(+x)^n=sum_(r=0)^n a_r x^r&b_r=1+(a_r)/(a_(r-1))&prod_(r=1)^n b_r=((101)^(100))/(100!),` then equals to: 99 (b) 100 (c) 101 (d) None of these

(1+x)^(n)=sum_(r=0)^(n)a_(r)x^(r)&b_(r)=1+(a_(r))/(a_(r-1))&prod_(r=1)^(n)b_(r)=((101)^(100))/(100!) then equals to: 99(b)100(c)101(d) None of these

If a_(n)=n(n!), then sum_(r=1)^(100)a_(r) is equal to

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)

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