Maximum sum of coefficient in the expansion of `(1-xsintheta+x^2)^n` is `1` b. `2^n` c. `3^n` d. `0`

Find the sum of the coefficients in the expansion of (1+2x+3x^2+ n x^n)^2dot

The coefficient of x^(n) in expansion of (1 + x)(1 - x)^(n) is

If the sum of the coefficients in the expansion of (1 -3x + 10x^2)^(n) is a and the sum of the coefficients in the expansion of (1 - x^(2))^(n) is b , then

The sum of coefficient in the expansion of (1+a x-2x^2)^n is (a)positive, when a<1a n dn=2k ,k in N (b)negative, when a<1a n dn=2k+1,k in N (c)positive, when a<1a n dn in N (d)zero, when a=1

Statement 1: The sum of coefficient in the expansion of (3^(-x//4)+3^(5x//4))^ni s2^ndot Statement 2: The sum of coefficient in the expansion of (x+y)^n i s2^ndot

if the sum of coefficients in the expansion of (x-2y+3z)^n is 128, then find the greatest coefficients in the expansion of (1+x)^ndot

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 the sum of the coefficients in the expansion of (a + b)^(n) is 4096, then the greatest coefficient in the expansion is

If |x|<1, then find the coefficient of x^n in the expansion of (1+x+x^2+x^3+....)^2dot

Prove that the coefficient of x^n in the expansion of (1+x)^2n is twice the coefficient of x^n in the expansion of (1+x)^2n-1 .