(p + 2)th term from the end in the binomial expansion ofx2−2x22n+1 is

$(p + 2)$ th term from the end in the binomial expansion of
${(x^{2} - \frac{2}{x^{2}})}^{2 n + 1}$ is

A
$^{2 n + 1} C_{2 n - n} (- 2)^{2 n - p} x^{2 p + 1 - 2 n}$
B
$^{2 n + 1} C_{2 n - n} (- 2)^{2 n - p} x^{2 n - 2 p}$
C
$^{2 n + 1} C_{2 n - p} (- 2)^{2 n - p} x^{2 n - 2 p + 1}$
D
$^{2 n + 1} C_{2 n - p} (- 2)^{2 n - p} x^{2 p - 1 + 2 n}$

Solution:

$(p + 2)$ th term from the end

$= [2 n + 2 - (p + 1)] th = (2 n - p + 1) th$

from the beginning

and $T_{2 n - p + 1} =^{2 n + 1} C_{2 n - p} {(x^{2})}^{2 n + 1 - (2 n - p)} {(- \frac{2}{x^{2}})}^{2 n - p}$

$=^{2 n + 1} C_{2 n - p} (- 2)^{2 n - p} x^{2 p + 1 - 2 n}$

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