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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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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Solution Summary
This solution is comprised of a detailed explanation of the Lucas numbers L_n . It contains step-by-step explanation of the Lucas numbers L_n defined by the equations L_1 = 1 and
L_n = F_(n+1) + F_(n-1) for each n > 2 and prove of the equation
L_1 + 2L_2 + 4L_3 +8L_4 + ... + 2^(n - 1) L_n = 2^n F_(n + 1) - 1
Solution contains detailed step-by-step explanation. Note is also given at end.
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Theory of Numbers (XIV)
Principle of Mathematical Induction
Fibonacci Number
...
Education
- BSc, Manipur University
- MSc, Kanpur University
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