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.

Algebra ->  Proofs -> 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.      Log On


   

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) About Me  (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.