# Convergence of a sequence

1. Jan 27, 2014

### zelmac

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. The attempt at a solution
I showed boundedness([0,6]) and found that in the case of convergence the limit is 2, but I dont know how to check its convergence... Any help is appreciated :)

2. Jan 27, 2014

### dirk_mec1

Show it's monotone.