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If the number of terms in the expansion of (1-(2)/(x)+(4)/(x²))ⁿ, x≠ 0, is 28, then the sum of the coefficients of all the terms in this expansion, is

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

Correct answer: 729

Solution

Number of terms in (1-2/x+4/x^2)^n is (n+1)(n+2)/2 = 28, so n=6. Sum of all coefficients = value at x=1 = (1-2+4)^6 = 3^6 = 729.

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