Binomial Theorem
Sum of products of binomial coefficients
MJAT_TS8_P2
Grade 12
Question:
If $f(n)=\displaystyle\sum_{i>j\geq 0}\binom{n+1}{i}\binom{n}{j}$, then:
A) $f(2)=16$
B) $f(5)=1001$
C) $f(6)=4096$
D) $f(1)=4$
Step-by-Step Solution
Key Concept: Rearrange: $f(n)=\sum_{i>j\geq 0}\binom{n+1}{i}\binom{n}{j}=\binom{2n+1}{n}+\binom{2n+1}{n-1}+\cdots=2^{2n}$.
A ✓, C ✓, D ✓. Answer: A, C, D.
Correct Answer: ACD