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In the expansion of (1 + x + 2x² + 4x⁴)²⁰, the coefficient of x⁷⁸ equals lambda * 2⁴⁰. Find the value of lambda.
- 11
- 10
- 8
- 4
Correct answer: 11
Solution
Splitting the expression as (1+x)²⁰ * (1+2x²)²⁰, we need pairs (a, b) with a from the first factor and b = 78-a from the second factor (b even), then sum the contributions to get lambda * 2⁴⁰.
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