9/10/2014 If the coefficients of the 4^th term of (x + y)¹¹ is 165, find the 5^th term.

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9/10/2014 Solution.
Since, in general, the relationship between coefficients of the (k + 1)^st and kth term of (x + y)ⁿ is ⁿC_k = ^{(n – (k – 1))}C_k·ⁿC_{(k – 1)}, we can find the 5^th term coefficient as: ^{11 – (4 – 1)}C₄·165 = 330 so that the 5^th term is: 330x⁷y⁴.