" If in the expansion of "(1-x)^(2n-1),a_(r)" denotes the coefficient of "x^(r)," then prove that "a_(r-1)+a_(2)n-s=0" ."

If in the expansion of (1-x)^(2n-1)a_(r) denotes the cofficient of x^(r) then prove that a_(r-1)+a_(2n-r)=0

If in the expansion of (1-x)^(2n-1) a_r denotes the coefficient of x^r then prove that a_(r-1) +a_(2n-r)=0

If in the expansion of (1-x)^(2n-1) , the coefficient of x^r is denoted by a_r , then show that a_(r-1)+a_(2n-r)=0 .

If in the expansion of (1-x)^(2n-1) , the coefficient of x^r is denoted by a_r then a_(r-1)+a_(2n-r)=

If a_(0), a_(1), a_(2),… are the coefficients in the expansion of (1 + x + x^(2))^(n) in ascending powers of x, prove that a_(0) a_(2) - a_(1) a_(3) + a_(2) a_(4) - …+ a_(2n-2) a_(2n)= a_(n+1) .

If a_(0), a_(1), a(2),… are the coefficients in the expansion of (1 + x + x^(2))^(n) in ascending powers of x, prove that a_(0) a_(2) - a_(1) a_(3) + a_(2) a_(4) - …+ a_(2n-2) a_(2n)= a_(n+1) .

If a_(r) is the coefficient of x^(r) in (1-2x+3x^(2))^(n), then sum_(r=0)^(2n)r*a_(r)=

If a_(r) be the coefficient of x^(r) in the expression of (1+bx^(2)+cx^(3))^(n),"then prove that" , a_(3)=nc

If a_(0),a_(1),a_(2),.... be the coefficients in the expansion of (1+x+x^(2))^(n) in ascending powers of x ,prove that : (i)a_(0)a_(1)-a_(1)a_(2)+a_(2)a_(3)-...=0

If a_(0),a_(1),a_(2) ,…, a_(2n) are the coefficients in the expansion of (1 + x + x^(2))^(n) in ascending power of x show that a_(0)^(2) - a_(1)^(2) + a_(2)^(2) -…+ a_(2n)^(2) = a_(n) .