May be I can try this one ... It can be proved using induction

s_n = ar^n

so ...

s_0 = a

s_1 = ar

s_2 = ar^2 .... a+ar = a(1+r) = ar^2

similarly

s_k = ar^k .... ar^(k-1) + ar^(k-2) = (ar^(k-2)) * (1+r) = (ar^(k-2) ) * r^2 = ar^k

Cheers!

Sunnycoder

Solved

Posted on 2006-04-18

Let r satisfy the equation r^2 = r + 1.

Show that the sequence s_n = ar^n, where A is constant, satisfies the fibonacci equation f_n = f_(n-1) + f_(n-2).

I'm not sure how to show this.

I know that f_1 = 1 & f_2 = 2

f_1 = 1

f_2 = 2

f_3 = f_2 + f_1

f_4 = f_3 + f_2

So

s_3 = s_2 + s_1 = Ar + Ar

s_4 = s_3 + s_2 = Ar + Ar + Ar

s_5 = s_4 + s_3 = Ar + Ar + Ar + Ar + Ar

s_6 = s_5 + s_4 = Ar + Ar + Ar + Ar + Ar + Ar + Ar + Ar

I'm not sure what i'm doing ;/

-Brian

Show that the sequence s_n = ar^n, where A is constant, satisfies the fibonacci equation f_n = f_(n-1) + f_(n-2).

I'm not sure how to show this.

I know that f_1 = 1 & f_2 = 2

f_1 = 1

f_2 = 2

f_3 = f_2 + f_1

f_4 = f_3 + f_2

So

s_3 = s_2 + s_1 = Ar + Ar

s_4 = s_3 + s_2 = Ar + Ar + Ar

s_5 = s_4 + s_3 = Ar + Ar + Ar + Ar + Ar

s_6 = s_5 + s_4 = Ar + Ar + Ar + Ar + Ar + Ar + Ar + Ar

I'm not sure what i'm doing ;/

-Brian

10 Comments

May be I can try this one ... It can be proved using induction

s_n = ar^n

so ...

s_0 = a

s_1 = ar

s_2 = ar^2 .... a+ar = a(1+r) = ar^2

similarly

s_k = ar^k .... ar^(k-1) + ar^(k-2) = (ar^(k-2)) * (1+r) = (ar^(k-2) ) * r^2 = ar^k

Cheers!

Sunnycoder

About 2 1/2yrs ago you used to help me with algebra...I've since advanced to higher levels of math, but good to see you again :)

Brian

By clicking you are agreeing to Experts Exchange's Terms of Use.

Title | # Comments | Views | Activity |
---|---|---|---|

Finite Automata | 10 | 33 | |

Using Excel Solver for Linear Programming | 3 | 73 | |

Formula to Randomize Data Set for Time Series Visual | 1 | 63 | |

Triangle - computing angles | 3 | 23 |

Join the community of 500,000 technology professionals and ask your questions.

Connect with top rated Experts

**12** Experts available now in Live!