Find the coefficient of `x^n` in `(1+x/(1!)+(x^2)/(2!)++(x^n)/(n !))^2` .

Statement 1: The coefficient of x^n is (1+x+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !))^3 is (3^n)/(n !) Statement 2: The coefficient of x^n ine^(3x)i s(3^n)/(n !)

Find the coefficient of x^k in 1 +(1 +x) +(1 +x)^2+.. +(1+x)^n (0 <=k<=n) .

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

If x^m occurs in the expansion (x+1//x^2)^ 2n then the coefficient of x^m is ((2n)!)/((m)!(2n-m)!) b. ((2n)!3!3!)/((2n-m)!) c. ((2n)!)/(((2n-m)/3)!((4n+m)/3)!) d. none of these

Coefficient of x^(6) in (1+x)(1+x^(2))^(2)(1+x^(3))^(3)…(1+x^(n))^(n) is

Find the coefficient of x^n in the polynomial (x+^n C_0)(x+3^n C_1)xx(x+5^n C_2)[x+(2n+1)^n C_n]dot

The coefficient of x^n in (1+x)^(101)(1-x+x^2)^(100) is nonzero, then n cannot be of the form 3r+1 b. 3r c. 3r+2 d. none of these

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