[" that "n" is not a multiple of "3" and "(1+x+x^(2))^(n)=],[" hen find the value of "sum_(r=0)^(n)(-1)^(r)*a_(r)*^(n)C_(r)]

Statement : if n in Nandn is not a multiple of 3 and (1+x+x^(2))^(n)=sum_(r=0)^(2n)a_(r)x^(r), then the value of sum_(r=0)^(n)(-1)^(r)ar^(n)C_(r) is zero Statement 2: The cofficient of x^(n) in the expansion of n=3k+1 or n=3k+2

If n in N such that is not a multiple of 3 and (1+x+x^(2))^(n) = sum_(r=0)^(2n) a_(r ). X^(r ) , then find the value of sum_(r=0)^(n) (-1)^(r ).a_(r).""^(n)C_(r ) .

If n in N such that is not a multiple of 3 and (1+x+x^(2))^(n) = sum_(r=0)^(2n) a_(r ). X^(r ) , then find the value of sum_(r=0)^(n) (-1)^(r ).a_(r).""^(n)C_(r ) .

Statement1: if n in Na n dn is not a multiple of 3 and (1+x+x^2)^n=sum_(r=0)^(2n)a_r x^r , then the value of sum_(r=0)^n(-1)^r a r^n C_r is zero Statement 2: The coefficient of x^n in the expansion of (1-x^3)^n is zero, if n=3k+1orn=3k+2.

Statement1: if n in Na n dn is not a multiple of 3 and (1+x+x^2)^n=sum_(r=0)^(2n)a_r x^r , then the value of sum_(r=0)^n(-1)^r a r^n C_r is zero Statement 2: The coefficient of x^n in the expansion of (1-x^3)^n is zero, if n=3k+1orn=3k+2.

If x+y= 1, then value of sum_(r=0)^(n)(r)(""^(n)C_(r))x^(n-r)y^(r) is

Find the sum sum_(r=1)^(n) r^(2) (""^(n)C_(r))/(""^(n)C_(r-1)) .

Find the sum sum_(r=1)^(n) r^(2) (""^(n)C_(r))/(""^(n)C_(r-1)) .

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

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