If `(1+x)^(n) = sum_(r=0)^(n) a_(2) x^(r) , b_(r) = 1 + a_(r)/(a_(r)-1)`
and `prod_(r=1)^(n) b_(r) = ((101)^(100))/(100!),` then the value of `n/20` is

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

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

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 f(x)=sum_(r=1)^(n) { r^(2) (""^(n)C_(r)- ^(n) C_(r-1))+ (2r+1) ^(n) C_(r)} and f(30)=30(2)^(lambda), then the value of lambda is

Let (1 + x)^(n) = sum_(r=0)^(n) a_(r) x^(r) . Then ( a+ (a_(1))/(a_(0))) (1 + (a_(2))/(a_(1)))…(1 + (a_(n))/(a_(n-1))) is equal to

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 x+y=1, prove that sum_(r=0)^n .^nC_r x^r y^(n-r) = 1 .

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 a_(n) = sum_(r=0)^(n) (1)/(""^(n)C_(r)) , find the value of sum_(r=0)^(n) (r)/(""^(n)C_(r))

Consider (1+x+x^(2)) ^(n) = sum _(r=0)^(2n) a_(r) x^(r) , "where " a_(0),a_(1), a_(2),…a_(2n) are real numbers and n is a positive integer. The value of a_(2) is