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The following summation are Fibonacci numbers starting with F₁ = 1. ( that is 1, 1, 2, 3, 5........):-
F₁ + F₂ + F₃ + .......... + Fₙ = Fₙ + 2.
Is this True or False?
If false how can you change it so it's true?

Respuesta :

sqdancefan

Answer:

  [tex]\textsf{the sum is }F_{n+2}-1[/tex]

Step-by-step explanation:

The given statement is FALSE.

Consider ...

  [tex]F_{n+2}=F_{n+1}+F_n\\\\F_n=F_{n+2}-F_{n+1}\\\\\displaystyle \sum_{i=1}^n{F_i}=\sum_{i=1}^n{F_{i+2}}-\sum_{i=1}^n{F_{i+1}}=F_{n+2}+\sum_{i=3}^{n+1}(F_i-F_i)-F_2\\\\\sum_{i=1}^n{F_i}=F_{n+2}-F_2 =\boxed{F_{n+2}-1}[/tex]

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