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If the expansion of (1-(2)/(x)+(4)/(x²))ⁿ, where x≠ 0, contains 28 terms, then what is the sum of the coefficients of all terms in that expansion?

1. 243
2. 729
3. 64
4. 2187

Correct answer: 729

Solution

Number of terms before collection is C(n+2,2)=28 -> n=6. Sum of all coefficients = value at x=1 = (1-2+4)^6 = 3^6 = 729.

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