Question

The value of \( \frac{100 C_{50}}{51} + \frac{100 C_{51}}{52} + \dots + \frac{100 C_{100}}{101} \) is :

• A. \( \frac{2^{100}}{100} \)
• B. \( \frac{2^{101}}{100} \)
• C. \( \frac{2^{101}}{101} \)
• D. \( \frac{2^{100}}{101} \)

Hint:

If the upper index of the sum of binomial coefficients is odd (like 101), the sum of the first half of terms is exactly equal to the sum of the second half.

Answer 1

The Correct Option is D