If `8sin^(3)xsin3x=sum_(r=0)^(n)a^(r)cosrx` is an identity in x, then n=

cos^3x.sin2x=sum_(m=1)^n(a_m)sin mx is an identity in x.

Suppose sin^3xsin3x=sum_(m=0)^n C_mcosm x is an identity in x , where C_0,C_1 ,C_n are constants and C_n!=0, the the value of n is ________

If cos^3xsin2x=sum_(r=0)^n a_xsin(r x),AAx in R then

sum_(r=0)^(n)(""^(n)C_(r))/(r+2) is equal to :

Find the sum sum_(r=0)^n^(n+r)C_r .

Find the sum sum_(r=0)^n^(n+r)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 ) .

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

If sum_(r=1)^(n) r(sqrt(10))/(3)sum_(r=1)^(n)r^(2),sum_(r=1)^(n) r^(3) are in G.P., then the value of n, is