Q. The value of$\frac{1}{81^{n}} - \frac{10}{81^{n}}{\ ^{2n}C}_{1}\ \frac{10^{2}}{81^{n}}{\ ^{2n}C}_{2} - \frac{10^{3}}{81^{n}}2{\ ^{2n}C}_{3} + ... + \frac{10^{2n}}{81^{n}}\ is$
A) 2
B) 0
C) $\frac{1}{2}$
D) 1
Explanation
(d)
$\frac{1}{81^{n}}\left( 1 - 10 \bullet \ ^{2n}C_{1} + 10^{2} \bullet \ ^{2n}C_{2} - 10^{3} \bullet \ ^{2n}C_{3} + \ldots + 10^{2n} \right)$
$= \frac{1}{({81)}^{n}}{(1 - 10)}^{2n} = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.