MCQ
If $\Big(\frac{\text{P}}{\text{q}}\Big)=0$ for $p < q p, \text{q}\in\text{W}$ then $\sum^\limits{\infty}_{\text{r}=0}\big(\frac{\text{n}}{2\text{r}})$
  • A
    $ 2^n $
  • $ 2^{n-1} $
  • C
    $ 2^{2 n-1} $
  • D
    $ 2^n C_n $

Answer

Correct option: B.
$ 2^{n-1} $

$\sum{^\text{n}}\text{C}_{2\text{r}}$
Is the sum of even odd term in the binomial expansion of $(1 + x)^n$
Hence
$\sum{^\text{n}}\text{C}_{2\text{r}}$will always be equal to $2^{n-1}$.

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