In the expansion of $ (1+ x)^{15}$, let $A$ be the sum of coefficients of odd powers of $x$ \(

Question

In the expansion of $ (1+ x)^{15}$, let $A$ be the sum of coefficients of odd powers of $x$ $B$ be the sum of coefficients of even powers of $x$ Without evaluating individual coefficients, Find $A$ and $B$. Generalise your result for $ (1 + x)^n$.

Accepted Answer

$A=B=16384$. In general, $A=B=2^{n-1}$ for positive integers $n$; for $n=0$, $A=0,\ B=1$.

Binomial Theorem - Sums of Coefficients in Polynomial Expansions

Binomial Theorem - Sums of Coefficients in Polynomial Expansions

Solution:

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