- 41

- 0

**[SOLVED] Convergence of a Sequence**

**1. Homework Statement**

Consider the following "recursively defined" sequence:

a1=0.3

a(n+1)=sqrt (an+1)

Compute the first first five terms and prove that it converges. Then, find the limit of the sequence.

Please see:

Problem 3, particularly parts c and d here for the complete problem:

http://rutcor.rutgers.edu/~ngoldberg/math152/ws0837.pdf [Broken]

**3. The Attempt at a Solution**

I would try to show that the sequence is increasing and bounded because that shows that it converges. I am not sure, however, how to go about doing this.

I think I am okay with finding the first five terms. I suppose the second term would be a2= sqrt (a1+1)=sqrt (1.3) and so on and so forth and it would get quite complicated.

I am not sure how to go about the proof and finding the limit.

Thank you.

Last edited by a moderator: