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2014-06-21T06:51:56-03:00
\boxed{f(n)=f(n-1)+f(n-2)}

f(1) = 1
f(2) = 1

primeiro olhando a f(1) 
f(1)=f(1-1)+f(1-2)=1\\\\f(0)+f(1)=1\\\\f(0)+1 = 1\\\\f(0)= 0

f(0) = 0
f(1) = 1
f(2) = 1

f(3) = f(3-1) + f(3-2)\\\\f(3)=f(2)+f(1)\\\\f(3)=1+1\\\\f(3)=2

f(0) = 0
f(1) = 1
f(2) = 1
f(3) = 2

f(4) =f(4-1) + f(4-2)\\\\f(4)=f(3)+f(2)\\\\f(4)=2+1\\\\f(4)=3

f(0) = 0
f(1) = 1
f(2) = 1
f(3) = 2
f(4) = 3

f(5) = f(5-1) + f(5-2)\\\\f(5) = f(4) +f(3)\\\\f(5)=3+2\\\\f(5)=5


f(0) = 0
f(1) = 1
f(2) = 1
f(3) = 2
f(4) = 3
f(5) = 5

veja que a sequencia segue um padrao
é sempre a soma dos dois resultados anteriores..

0+1 = 1 = f(2)
1+1 = 2 = f(3)
2+1 = 3 = f(4)
3+2 = 5 = f(5)

logo 
f(6) = 5+3 = 8
f(7) = 8+5 = 13
f(8) = (13 +8) = 21
f(9) = 21+13  = 34
f(10) = 34+21 = 55
f(11) = 55+34=89
f(12) = 89+55 =144
f(13) = 144+89 =233

f(8) + f(13) = 21+233 = 254


2 5 2