Convergence of a Sequence: How to Determine and Find the Limit?

[zelmac]

Homework Statement

Check whether the sequence $a_{1}=\alpha ,\alpha > 0, a_{n+1}=6*\frac{a_{n}+1}{a_{n}+7}$ converges and find its limit if it does, depending on α.

Homework Equations

The Attempt at a Solution

I showed boundedness([0,6]) and found that in the case of convergence the limit is 2, but I don't know how to check its convergence... Any help is appreciated :)

 

[dirk_mec1]

Show it's monotone.