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The sum of the series 2·²⁰C₀ + 5·²⁰C₁ + 8·²⁰C₂ + 11·²⁰C₃ +... + 62·²⁰C₂₀ is equal to -

1. 2²³
2. 2²⁵
3. 2²⁶
4. 2²⁴

Correct answer: 2²⁵

Solution

The series can be expressed as a combination of binomial coefficients and a linear function, which can be evaluated using the binomial theorem and properties of generating functions. The correct option, 2²⁵, arises from the evaluation of the series, where the coefficients represent a linear transformation of the binomial expansion.

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