Sequences a_n and b_n are defined in the follwing way:(adsbygoogle = window.adsbygoogle || []).push({});

a_1=x;

b_1=y;

where 0<x<y

and:

a_(n+1) = (a_n+b_n)/2

b_(n+1) = sqrt(a_(n+1)+b_n)

Proof, that both sequences are convergent to the same limit and find this limit.

Thanks a lot for any help.

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# Finding limit

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