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In the power-series expansion of (1 - 9x + 20x²)⁻¹, the coefficient of xⁿ is

1. 5ⁿ - 4ⁿ
2. 5ⁿ⁺¹ - 4ⁿ⁺¹
3. 5ⁿ⁻¹ - 4ⁿ⁻¹
4. None of these

Correct answer: 5ⁿ⁺¹ - 4ⁿ⁺¹

Solution

The correct option is derived from the geometric series expansion, where the function can be expressed in terms of its roots. The coefficients of the series correspond to the contributions from the roots of the polynomial, leading to the formula for the coefficients being in the form of powers of the roots, specifically resulting in the expression for the coefficient of xⁿ being 5ⁿ⁺¹ - 4ⁿ⁺¹.

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