Kenneth S. answered • 03/21/18

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Expert Help in Algebra/Trig/(Pre)calculus to Guarantee Success in 2018

a. since the beginning of the Fibonacci sequence is 0,1,1,2,3,5, etc. it's obvious that every positive integer can be expressed as the sum of ONE OR MORE distinct non-consecutive Fibonacci numbers. example: 4 = 1 + 3; 6 = 1+5; 7 = 2+5; 9 = 1+3+5

b. Let F(k+1) be 55; then the sum of these non-consecutive Fibonacci predecessors 34, 13, 5, 2, 1 is also 55. 34 is F(k), and this sum is NOT STRICTLY LESS THAN F(k+1).

**I believe that this counterexample disproves the second assertion in your submitted 'question.'**