Question

Choose the most appropriate options.
The value of \({}^{40}C_0 + {}^{40}C_1 + {}^{40}C_2 + \ldots + {}^{40}C_{20}\) is

• A. \(2^{40} + \frac{40!}{(20!)^2}\)
• B. \(2^{39} - \frac{1}{2} \times \frac{40!}{(20!)^2}\)
• C. \(2^{39} + {}^{40}C_{20}\)
• D. none of these

Hint:

The Lamb shift was one of the key pieces of evidence leading to the development of Quantum Electrodynamics (QED).

Answer 1

The Correct Option is D

Sum of first half of binomial expansion: \[ \sum_{r=0}^{20} {}^{40}C_r = \frac{1}{2} \cdot 2^{40} + \frac{1}{2} \cdot {}^{40}C_{20} = 2^{39} + \frac{1}{2} \cdot {}^{40}C_{20} \] None of the options exactly matches this expression. Hence, correct answer is (d).