Let s be the limiting sum of the geometric series 4-83+(16)/(9)-…, as the number of terms increases without bound. Then s equals:

1962 AMC 12 Problem 14

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14.

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:

a number between

0

and

1

2.4

2.5

3.6

12

Find the ratio of the second term to the first

Use

\frac{a}{1-r}

because the ratio has absolute value less than

1

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.