11/07/2009, 09:31 AM

Let me rephrase in my words:

We consider the linear functions on (k-1,k) determined by and , they are given by:

.

As f is concave for , and as is strictly increasing we have also .

On the other hand we know that for , hence and for .

We have now for . But I think that does not directly show the convergence .

Any ideas?

We consider the linear functions on (k-1,k) determined by and , they are given by:

.

As f is concave for , and as is strictly increasing we have also .

On the other hand we know that for , hence and for .

We have now for . But I think that does not directly show the convergence .

Any ideas?