Which one of the following is the <strong>GREATEST</strong> coefficient in the expansion of (1+x)^{100}?
- A. The coefficient of x^{100}
- B. The coefficient of x^{99}
- C. The coefficient of x^{51}
- D. The coefficient of x^{50} ✓
Correct Answer: D. The coefficient of x^{50}
Explanation
In the binomial expansion of (1+x)^n where n is an even integer, the greatest binomial coefficient occurs at the middle term, which is T_{\frac{n}{2}+1}. For n=100, the greatest coefficient is \binom{100}{50}, which is the coefficient of x^{50}.
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