AMC8 1996

AMC8 1996 · Q4

AMC8 1996 · Q4. It mainly tests Fractions, Arithmetic sequences basics.

\(\frac{2+4+6+\cdots+34}{3+6+9+\cdots+51} =\)

(A) \(\frac{1}{3}\) \(\frac{1}{3}\)

(B) \(\frac{2}{3}\) \(\frac{2}{3}\)

(D) \(\frac{17}{3}\) \(\frac{17}{3}\)

(E) \(\frac{34}{3}\) \(\frac{34}{3}\)

Answer

Correct choice: (B)

正确答案：（B）

Solution

\(2 + 4 + 6 + \cdots + 34 = 2(1 + 2 + 3 + \cdots + 17)\) \(3 + 6 + 9 + \cdots + 51 = 3(1 + 2 + 3 + \cdots + 17)\) so the ratio is \(\frac{2}{3}\).

\(2 + 4 + 6 + \cdots + 34 = 2(1 + 2 + 3 + \cdots + 17)\) \(3 + 6 + 9 + \cdots + 51 = 3(1 + 2 + 3 + \cdots + 17)\) 所以比值为 \(\frac{2}{3}\)。

Topics