Question

If binomial coefficients of three consecutive terms of (1+x)ⁿ are in H.P., then the maximum value of n is

• A. \(1\)
• B. \(2\)
• C. \(0\)
• D. None of these

Hint:

Use harmonic mean condition: (2ab)/(a+b).

Answer 1

The Correct Option is B

Let the coefficients be \( \binom{n}{r-1}, \binom{n}{r}, \binom{n}{r+1} \).

H.P. condition:
\( \dfrac{2}{\binom{n}{r}} = \dfrac{1}{\binom{n}{r-1}} + \dfrac{1}{\binom{n}{r+1}} \)
Solving gives maximum possible \( n = 2 \).