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The Lucas numbers L_n are defined by the equations L_1 = 1 and L_n = F_(n+1) + F_(n-1) for each n > or equal to 2. Prove that L_1 + 2L_2 + 4L_3 +8L_4 + … + 2^(n – 1) L_n = 2^n F_(n + 1) – 1

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November 14th, 2022

Theory of Numbers (XIV)
Principle of Mathematical Induction
Fibonacci Number
Lucas number

The Lucas numbers L_n are defined by the equations L_1 = 1 and L_n = F_(n+1) + F_(n-1) for each n > or equal to 2.
Prove that
L_1 + 2L_2 + 4L_3 +8L_4 + … + 2^(n – 1) L_n = 2^n F_(n + 1) – 1

See the attached file.

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