Binomial Theorem
Greatest Binomial Coefficient
Premium Question
Grade 11
Question:
The greatest binomial coefficient in the expansion of $(1 + x)^{2n}$ is:
(1) $\binom{2n}{n}$
(2) $\binom{2n}{n - 1}$
(3) $\binom{2n}{n + 1}$
(4) $2^{2n}$
Step-by-Step Solution
Key Concept: Recall that the binomial coefficients $\binom{2n}{r}$ increase up to the middle term and then decrease symmetrically — identify the value of $r$ that corresponds to this single middle term when the total number of terms is odd.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)