Question

The term independent of x in the expansion of $(1+x{)}^n{(1+\frac{1}{x})}^n$ is

• A. $C_0^2+2C_1^2+3C_2^2+....+(n+1)C_n^2$
• B. $(C_0+c_1+....+c_n{)}^2$
• C. $c_0^2+C_1^2+.....+c_n^2$
• D. $Noneoftheabove$

Answer 1

The correct option is C $c_0^2+C_1^2+.....+c_n^2$

$(1+x{)}^n{(1+\frac{1}{x})}^n=(c_0+c_{1}x+c_2{x}^2+.....+c_n{x}^n)\times (C_0+\frac{C_1}{x}+\frac{C_2}{x^2}+...+\frac{C_n}{x^n})TermindependentofxontheRHS=C_0^2+C_1^2+C_2^2+....+C_n^2$