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Part of ALG-06 — Binomial Theorem

Middle Term

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For (x + y)^n:

  • If n is even: One middle term = T_{n/2 + 1}
  • If n is odd: Two middle terms = T_{(n+1)/2} and T_{(n+3)/2}

The middle term typically has the largest absolute value when x and y have comparable magnitudes, and always involves the largest binomial coefficient C(n, floor(n/2)).

Example: In (1 + x)^6, middle term is T_4 = C(6,3)*x^3 = 20x^3. In (1 + x)^7, middle terms are T_4 = C(7,3)*x^3 = 35x^3 and T_5 = C(7,4)*x^4 = 35x^4.

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