(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let D_k=(r_k-1/2^k,r_k+1/2^k), where r_k=1/k. Then prove that

D=union_k=1 to ∞ (D_k) has volume.

2. Relevant equations

3. The attempt at a solution

I tried to solve this problem by showing bd(D) has measure zero.

So I wanted to show that bd(D) is contained in union_k=1 to ∞(bd(D_k)). Of course since bd(D_k)={r_k-1/2^k, r_k+1/2^k}, union_k=1 to ∞(bd(D_k)) has measure zero. But how can I show this? Or is there another solution to this problem?

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# Homework Help: Prove that this set has volume.

Can you offer guidance or do you also need help?

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