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

If (1+x)^(n)=sum_(r=0)^(n)a_(r)x^(r) and b_(r)=1+(a_(r))/(a_(r-1)), and prod_(r=1)^(n)b_(r)=((101)^(100))/(100!) then n equals:

If sum_(r=1)^n t_r= (n(n+1)(n+2))/3 then sum _(r=1)^oo 1/t_r= (A) -1 (B) 1 (C) 0 (D) none of these

If (1-x^2)^n=sum_(r=0)^na_rx^r(1-x)^(2n-r) , then a_r is equal to

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

If sum_(r=0)^(n-1)log_(2)((r+2)/(r+1)) =prod_(r=10)^(99)log_(r) (r+1), then 'n' is equal to (A) 4 (B) 3 (C) 5 (D) 6

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