Recusive help

**erinneedshelp** · November 21st 2009, 11:55 AM

I am needing help with this

Find f 2, f 3, f 4, and f 5 if f is defined recursively by f 0 = f 1 = 1 and for n = 1,2
f n+1 = ( f n ) 2 + ( f n-1 ) 3

**Soroban** · November 21st 2009, 01:27 PM

Hello, erinneedshelp!

Just follow the directions.
Exactly where is your difficulty?

Given: . $f_0 \:=\:f_1 \:=\:1, \quad f_{n+1} \:=\:(f_n)^2 + (f_{n-1})^3\;\;\text{ for }n \geq 2$

Find: . $f_2,\;f_3,\;f_4,\:f_5$

. . $\begin{array}{ccc|c} f_n &=& (f_{n-1})^2 + (f_{n-2})^3 & f_n \\ \hline &&& f_0 \:=\: 1 \\ &&& f_1 \:=\: 1 \\ f_2 &=& 1^2 + 1^3 & f_2 \:=\:2 \\ f_3 &=& 2^2 + 1^3 & f_3 \:=\:5 \\ f_4 &=& 5^2 + 2^3 & f_4 \:=\:33 \\ f_5 &=& 33^2 + 5^3 & f_5 \:=\:1214 \end{array}$

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