if `(1-x^3)^n=sum_(r=0)^n a_rx^r (1-x)^(3n-2r),` where n `epsilonN ` then find `a_r`.

If (1-x^(2))^(n)=sum_(r=0)^(n)a_(r)x^(r)(1-x)^(2n-r), then a_(r) is equal to ^(n)C_(r) b.^(n)C_(r)3^(r) c.^(2n)C_(r) d.^(n)C_(r)2^(r)

If ninN,ngt4 and (1-x^(3))^(n)=sum_(r=0)^(n)a_(r)x^(r)(1-x)^(3n-2r) , then sum_(r=0)^(n)a_(r)=lambda^(n) , find lambda.

If (1-x^(3))^(n)=underset(r=0)overset(n)(sum)a_(r)x^(r)(1-x)^(3n-2r) , then the value of a_(r) , where n in N is

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of

Find sum_(r=0)^n(r+1)*"^nC_rx^r

If (1+x+x^(2)+x^(3))^(n)=sum_(r=0)^(3n)b_(r)x^(r) and sum_(r=0)^(3n)b_(r)=k, the n sum_(r=0)^(3n)rb_(r)

For x in(0,(pi)/(4)). Let S_(n)=sum_(r=1)^(2n)sin(sin^(-1)x^(3r-2)),C_(n)=sum_(r=1)^(2n)cos(cos^(-1)x^(3r-1)) and T_(n)=sum_(r=1)^(2n)tan(tan^(-1)x^(3r)) where n in N and n>=3

If x+y=1, then sum_(r-0)^(n)rnC_(r)x^(r)y^(n-r) equals

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