Question

In the expansion of $(1+x{)}^{50}$, the sum of the coefficients of odd powers of $x$ is

• A. $2^{26}$
• B. $2^{49}$
• C. $2^{50}$
• D. $2^{51}$

Answer 1

Answer: (B)

$2^{49}$

We know that ${(1+x)}^{50}=1+x+x^2+...+x^{50}$,

Substituting $x=1$ gives,

$2^{50}=1+2+2^2+...+2^{50}$,

Substituting $x=-1$ gives,

$0=1-2+2^2-2^3...+2^{50}$,

substracting the two equations gives,

$2^{50}=2(1+2+2^3+...+2^{49})⟹1+2+2^3+...+2^{49}=2^{49}$