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Thread: Recusive help

  1. #1
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    Recusive help

    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
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  2. #2
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    Hello, erinneedshelp!

    Just follow the directions.
    Exactly where is your difficulty?


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

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

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

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