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:

H.P. ⇒ reciprocals in A.P.

Answer 1

The Correct Option is B

Step 1: Let coefficients be \[ {n\choose r-1},{n\choose r},{n\choose r+1} \]
Step 2: H.P. condition: \[ \frac2{{n\choose r}}=\frac1{{n\choose r-1}}+\frac1{{n\choose r+1}} \]
Step 3: Solving gives \(n\le2\).