Use the recursive definition for Fibonacci numbers and deductive reasoning to verify that, for Fibonacci numbers, 2 F n − F n − 2 = F n + 1 for n ≥ 3 . Hint : By definition. F n + 1 = F n + F n − 1 and F n = F n − 1 + F n − 2 .
Use the recursive definition for Fibonacci numbers and deductive reasoning to verify that, for Fibonacci numbers, 2 F n − F n − 2 = F n + 1 for n ≥ 3 . Hint : By definition. F n + 1 = F n + F n − 1 and F n = F n − 1 + F n − 2 .
Solution Summary: The author calculates the average number of new planets per month that have been detected since April 1,2011.
Use the recursive definition for Fibonacci numbers and deductive reasoning to verify that, for Fibonacci numbers,
2
F
n
−
F
n
−
2
=
F
n
+
1
for
n
≥
3
. Hint: By definition.
F
n
+
1
=
F
n
+
F
n
−
1
and
F
n
=
F
n
−
1
+
F
n
−
2
.
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