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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For a proof that a monotonous bounded sequence converges see:
For the geometric series sum see:
I use them both in the ...
Convergent Sequences and Limits are investigated. The solution is detailed and well presented.