1962 AMC 12 第 14 题

Question

当项数无限增加时，设等比级数

4-\dfrac83+\dfrac{16}{9}-\cdots

的极限和为

s

。则

s

等于：

Let

s

be the limiting sum of the geometric series

4-\dfrac83+\dfrac{16}{9}-\cdots,

as the number of terms increases without bound. Then

s

equals:

0

与

1

之间的一个数

a number between

0

and

1

2.4

2.5

3.6

12

求第二项与第一项之比

Find the ratio of the second term to the first

由于公比的绝对值小于

1

，使用

\frac{a}{1-r}

Use

\frac{a}{1-r}

because the ratio has absolute value less than

1

首项为

4

，公比为

-\frac{2}{3}

。因此

s=\frac4{1-(-\frac{2}{3})}=\frac{12}{5}=2.4\text{。}

所以正确答案是 B。

The first term is

4

and the common ratio is

-\frac{2}{3}.

Thus

s=\frac4{1-(-\frac{2}{3})}=\frac{12}{5}=2.4.

Therefore, the correct answer is B.

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