Question:
The arithmetic mean of \( ^nC_0, ^nC_1, \ldots, ^nC_n \) is
The arithmetic mean of \( ^nC_0, ^nC_1, \ldots, ^nC_n \) is
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Sum of binomial coefficients = \(2^n\).
Updated On: May 1, 2026
- \( \frac{2^n}{n+1} \)
- \( \frac{2^n}{n} \)
- \( \frac{2^{n-1}}{n+1} \)
- \( \frac{2^{n-1}}{n} \)
- \( \frac{2^{n+1}}{n} \)
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The Correct Option is A
Solution and Explanation
Concept: Mean = Sum number of terms.
Step 1: Total terms: \[ n+1 \]
Step 2: Sum: \[ \sum_{r=0}^n ^nC_r = 2^n \]
Step 3: Mean: \[ = \frac{2^n}{n+1} \]
Step 4: No simplification needed.
Step 5: Final result obtained.
Step 1: Total terms: \[ n+1 \]
Step 2: Sum: \[ \sum_{r=0}^n ^nC_r = 2^n \]
Step 3: Mean: \[ = \frac{2^n}{n+1} \]
Step 4: No simplification needed.
Step 5: Final result obtained.
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