Recursive sequence limit challenge

Hi, I saw this problem in Coursera's Calculus II by the Ohio State University:

Most of us are familiar with the Fibonacci Sequence

Now we can build an if we took the limit

First I want to know how to compute that kind of limit, I tried some of the things I have at hand(That aren't very much since I haven't done a googling about sequence limits nor continue with the course) but without results.

The other limit I want you to check is form the so-called Tribonacci sequence:

then, as you can guess, what is the value of ?

A lot of thanks and

Regards,

ManuelSG :)

1 Attachment(s)

Re: Recursive sequence limit challenge

Hi,

In order to follow the solution in the attachment, you need to know about linear homogeneous constant coefficient recurrence relations -- Recurrence relation - Wikipedia, the free encyclopedia

Attachment 29627