AMC 8 2017 Problem 5
AMC8 2017 年第 5 题
表达式与运算★☆☆☆☆
What is the value of the expression shown below?
下面表达式的值为多少
？
- A.1020
- B.1120
- C.1220
- D.2240
- E.3360
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
It is well known that the sum of all numbers from 1 to is . Therefore, the denominator is equal to . Now, we can cancel the factors of 2, 3, and 6 from both the numerator and denominator, only leaving . This evaluates to 1120.
First, we evaluate 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 to get 36. We notice that 36 is 6 squared, so we can factor the denominator like then cancel the 6s out to get . Now that we have escaped fraction form, we multiply . Multiplying these, we get 1120. for minor edits
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