AMC 8 2025 Problem 20

AMC8 2025 年第 20

数列与规律★★★☆☆
Sarika, Dev, and Rajiv are sharing a large block of cheese. They take turns cutting off half of what remains and eating it: first Sarika eats half of the cheese, then Dev eats half of the remaining half, then Rajiv eats half of what remains, then back to Sarika, and so on. They stop when the cheese is too small to see. About what fraction of the original block of cheese does Sarika eat in total?
和Rajiv正在分享一大块奶酪。他们轮流切下奶酪剩余部分的一半并吃掉:首先Sarika吃掉一半奶酪,接着Dev吃掉剩余部分的一半,随后Rajiv吃掉剩余部分的一半,然后又轮到Sarika,如此循环往复,直到奶酪小到看不见为止。请问Sarika一共大约吃掉了这块奶酪的几分之几?
  1. A.47\displaystyle \frac{4}{7}
  2. B.35\displaystyle \frac{3}{5}
  3. C.23\displaystyle \frac{2}{3}
  4. D.34\displaystyle \frac{3}{4}
  5. E.78\displaystyle \frac{7}{8}

正确答案 · Correct Answer

A

解析 · Solution

解析整理中

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