Q. The greatest coefficient in the expansion of ${(1 + x)}^{2n}\$is
A) $\ ^{2n}C_{n}$
B) $\ ^{2n}C_{n + 1}$
C) $\ ^{2n}C_{n - 1}$
D) $\ ^{2n}C_{2n - 1}$
Explanation
(a)
Since, ${(1 + x)}^{2n} = \ ^{2n}C_{0} + \ ^{2n}C_{0} + \ ^{2n}C_{1}x + \ ^{2n}C_{2}x^{2}$
+....$+ \ ^{2n}C_{n}x^{n} +$…$\ ^{2n}C_{2n}x^{2n}$
Total number of terms in the expansion $= 2n + 1$
$\therefore(n + 1)$th term is middle term. This term has greatest coefficient.
Hence, required greatest coefficient $= \ ^{2n}C_{n}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.