網頁2013年3月21日 · Problem11: Let whichconsists allnumbers which do decimalexpansion. Find hasmeasure samereason Cantorset. We can construct Cantor-likeiterates. firstiterate unitinterval; secondhas length1/10 deleted, lengths3/10 6/10remaining. deletedinterval … 網頁2024年7月21日 · Solution: (a) Since ∑ k = 1 ∞ a k converges, the sequence ( a n) converges to zero by k t h -term Test. Hence ( a n) is bounded by Proposition 3.20. Hence there exists α > 0 such that a k < α for all k. In particular, we have 0 < a k 2 < α a k for all k. Since ∑ k = 1 ∞ a k converges, so does ∑ k = 1 ∞ α a k converges.

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