# Real Analysis : Convergent Sequences and Limits

Prove the sequence defined by a1 = 0, a2=1 and a(n+2)= (a(n+1)+a(n))/2 for n>=0, converges and find the limit.

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https://brainmass.com/math/real-analysis/real-analysis-convergent-sequences-limits-34399

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The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

For a proof that a monotonous bounded sequence converges see:

http://www-history.mcs.st-and.ac.uk/~john/analysis/Lectures/L8.html

For the geometric series sum see:

http://mathworld.wolfram.com/GeometricSeries.html

I use them both in the ...

#### Solution Summary

Convergent Sequences and Limits are investigated. The solution is detailed and well presented.