Question

Consider the expansion of $(1+x{)}^{2n+1}$
The sum of the coefficients of all the terms in the expansion is

• A. $2^{2n-1}$
• B. $4^{n-1}$
• C. $2\times 4^n$
• D. None of the above

Answer 1

Answer: (C)

$2\times 4^n$

We can get the sum of all coefficients by putting $x=1$ in the expansion, because for calculating the coefficients we need the terms independent of $x$.

To find the sum of coefficients of all terms, put $x=1$ in the given expression$(1+x{)}^{2n+1}$ we get

$2^{2n+1}={2.2}^{2n}={2.4}^n$

Hence, C is the correct option.