(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need tounderstandand prove the following: That if a>1 the function diverges, except for a special case x_0= b/(1-a). Then if a=-1 diverges for some cases and converges if x_0 is b/2. Again, not to clear on this.

2. Relevant equations

lim n →∞ a^n(x_0+b/(a-1))-b/(a-1)

3. The attempt at a solution

For a>1, then we just need to look at x_0 and b/(a-1)? If x_0 > b/(a-1), then this is + and still diverges, then we rely on -b/(a-1)? I am kind of confused and any help would be appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Iteration, linear function. convergence and divergence

**Physics Forums | Science Articles, Homework Help, Discussion**