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If the number of distinct terms in the expansion of (x + 1 + 1/x)ⁿ (where n is a positive integer) is 17, find n.
- 6
- 7
- 8
- 9
Correct answer: 8
Solution
Writing the expression as (x²+x+1)/xⁿ, the powers of x range from x^(-n) to xⁿ, yielding 2n+1 distinct terms. Setting 2n+1 = 17 gives n = 8.
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