If `(1+x) ^(15) =a_(0) +a_(1) x +a_(2) x ^(2) +…+ a_(15) x ^(15),` then the value of `sum_(r=1) ^(15) r . (a_(r))/(a _(r-1))` is-

If (1+x+x^(2))^(3n+1)=a_(0)+a_(1)x+a_(2)x^(2)+…a_(6n+2)x^(6n+2) , then find the value of sum_(r=0)^(2n)(a_(3r)-(a_(3r+1)+a_(3r+2))/2) is______.

If (1+x+x^(2))^(3n+1)=a_(0)+a_(1)x+a_(2)x^(2)+…a_(6n+2)x^(6n+2) , then find the value of sum_(r=0)^(2n)(a_(3r)-(a_(3r+1)+a_(3r+2))/2) is

(1+x+x^(2)+x^(3))^(5)=a_(0)+a_(1)x+a_(2)x^(2)+....+a_(15)x^(15), then a_(10) equals 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 (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

Let (x + 10)^(50) + (x - 10)^(50) = a_(0) + a_(1) x + a_(2)X^(2) + ….. + a_(50) x^(50) , for all x in R , then (a_(2))/(a_(0)) is equal to

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

If (x^(2)+x+1)/(1-x) = a_(0) + a_(1)x+a_(2)x^(2)+"…." , then sum_(r=1)^(50) a_(r) equal to