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Let (1 + x + 2x^2)^20 = a0 + a1x + a2x^2 + ... + a40x^40 Then a1 + a3 + a5 + ... + a37 is equal to

1. 2^20(2^20 - 21)
2. 2^19(2^20 - 21)
3. 2^19(2^20 + 21)
4. 2^20(2^20 + 21)

Correct answer: 2^19(2^20 - 21)

Solution

The expression (1 + x + 2x^2)^20 can be evaluated for the sum of coefficients of the odd-powered terms by substituting x with 1 and -1, then using the formula for the sum of coefficients. The correct option is derived from this calculation, which yields 2^19(2^20 - 21) as the sum of the coefficients of the odd powers.

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