Binomial Theorem
Properties of Binomial Coefficients
Premium Question
Grade 11
Question:
The value of $\binom{n}{r} + \binom{n}{r - 1}$ equals:
(1) $\binom{n + 1}{r}$
(2) $\binom{n + 1}{r - 1}$
(3) $\binom{n}{r + 1}$
(4) $\binom{n - 1}{r}$
Step-by-Step Solution
Key Concept: This is one of the most fundamental identities in combinatorics — recall Pascal's rule, which expresses how each entry of Pascal's triangle is built from the two entries directly above it.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)