If ( P q )=0 for p < q p, q then ^ _ r=0 ( n 2r ) - Vidyadip

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
$2^{2 \mathrm{n}-1}$
D
$2^n C_n$

✓

Answer

Correct option: B.

$2^{n-1}$

$2^{n-1}$

Solution:
$\sum{^\text{n}}\text{C}_{2\text{r}}$
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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