Question

If $C_0,C_1,C_2...,C_n$ denote the binomial coefficients in the expression of $(1+x{)}^n$, then find the sum of $C_0+C_1+C{C}_2+....C_n+..$

• A. $2^{n-1}$
• B. $2^n$
• C. $2n+1$
• D. 0

Answer 1

The correct option is B $2^n$

We know ${(1+x)}^n=C_0$ $+$ $C_1$ $x+$ $C_2$$x^2$....... $+$ $C_n$$x^n$

To find $C_0+C_1+C_2+....+C_n$, put $x=1$

Thus $C_0$ $+$ $C_1$ $+$ $C_2$ $+$ .......... $+$ $C_n$ $=2^n$

Hence, option B is correct.