SOLUTION: Let f_n be the nth Fibonacci number. Show that for every natural n
f_1 + f_2 + . . . + f_n = f_(n+2) − 1.
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Question 1021450: Let f_n be the nth Fibonacci number. Show that for every natural n
f_1 + f_2 + . . . + f_n = f_(n+2) − 1.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
You can show by induction on n.
When n = 1, we have 
, which is true since 1 = 2-1.
For some 
, assume by hypothesis that 
. Adding 
to both sides gives 
, so the expression holds for k+1.
Therefore, the equation holds for all natural n.
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