Answer: T₃.
- A T₄
- B T₅
- C T₃
- D T₆
Correct answer: C. T₃
Explanation: With x=1/5, 5x=1, so T(r+1)=C(10,r)*310-r. Computing directly: T1=310=59049, T2=10*39=196830, T3=45*38=295245, T4=120*37=262440. Since T3 exceeds both T2 and T4, T3 is the largest term.
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