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 ________

Suppose sin^(3)x sin3x=sum_(m=0)^(n) C_(m) cos mx is an idedntity in x , where C_(0),….C_(n) are constant and C_(n)ne0 then the value of n is ___________

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

If sin^3x sin3x= sum_(n=0)^6 c_n cos^n x where c_0, c_1, c_2,...c_6 are constants. then find the value of c_4

If (1+x)^n=sum_(r=0)^n C_r x^r , then prove that C_1+2C_2+3C_3+....+n C_n=n2^(n-1)dot .

If (1 + x + x^2)^n = (C_0 + C_1x + C_2 x^2 + ............) then the value of C_0 C_1-C_1C_2+C_2C_3.....

Prove that sum_(r=0)^n^n C_rsinr xcos(n-r)x=2^(n-1)sin(n x)dot

If (1+x)^n=sum_(r=0)^n^n C_r , show that C_0+(C_1)/2++(C_n)/(n+1)=(2^(n+1)-1)/(n+1) .

If C_o C_1, C_2,.......,C_n denote the binomial coefficients in the expansion of (1 + x)^n , then the value of sum_(r=0)^n (r + 1) C_r is

Find the sum 3^n C_0-8^n C_1+13^n C_2xx^n C_3+dot

Prove that sum_(r=0)^(n) ""^(n)C_(r )sin rx. cos (n-r)x = 2^(n-1) xx sin nx .