Answer: Even.
- A Even
- B Odd
- C Cannot be determined
- D Always 1
Correct answer: A. Even
Explanation: (5+2sqrt6)<sup>n</sup> + (5-2sqrt6)<sup>n</sup> is always an even integer because only even-power terms survive (irrational terms cancel), and the result is a sum of integers.
Row n of Pascal's triangle gives the coefficients nC0, nC1, ..., nCn for the expansion of (a+b)ⁿ; each number is the sum of the two numbers diagonally above it, a direct visual proof of the identity nCr = (n-1)C(r-1) + (n-1)Cr.
Concept context
Expansion of (a+b) n , general term, middle term, binomial coefficients, and greatest term