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[SOLVED] Convergence of a Sequence
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
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.
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
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.
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