Answer: 1.
- A 0
- B 2
- C 3
- D 1
Correct answer: D. 1
Explanation: 3100 = (4-1)100 = 4100 - 100 x 499 + ... + (-1)100 = 4100 - ... + 1. All terms except the last contain factor 4. So 3100 mod 4 = 1.
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