Problem

The Lucas numbers, named after François-Eduoard-Anatole Lucas (see Chapter 7 for a biograp...

The Lucas numbers, named after François-Eduoard-Anatole Lucas (see Chapter 7 for a biography), are defined recursively by

with L1 = 1 and L2 = 3. They satisfy the same recurrence relation as the Fibonacci numbers, but the two initial values are different.

Find and prove a formula for the sum of the first n Lucas numbers with odd indices when n is a positive integer.

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Solutions For Problems in Chapter 1.4

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