# Would you please tell me what's the limit of #(V_n-U_n)# as #n# approaches positive infinity ? PS: #U_(n+1)= sqrt(U_nV_n)# and #V_(n+1)=(U_n+V_n)/2#

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Here are my thoughts:

I'm not sure if this is helpful, but feedback is welcome.

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It follows that

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The limit of (V_n-U_n) as n approaches positive infinity is 0.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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