Question

Which geometric series represents 0.4444... as a fraction?

Answer 1

Answer: It can be expressed as

$\frac{4}{10}+\frac{4}{100}+\frac{4}{1000}+........$

Step-by-step explanation:

Since we have given that 0.44444.......

We need  geometric series that represents as a fraction.

so, it can be written as

0.4+0.04+0.004+0.0004...............

But as we are required to write it as a fraction , So, it becomes,

$\frac{4}{10}+\frac{4}{100}+\frac{4}{1000}+\frac{4}{10000}............$

and it is a geometric series.

Because it has first term = a = $\frac{4}{10}$

and common ratio = r = $\frac{a_2}{a_1}=\frac{\frac{4}{100}}{\frac{4}{10}}=\frac{1}{10}$

Hence, it can be expressed as

$\frac{4}{10}+\frac{4}{100}+\frac{4}{1000}+........$

Answer 2

The geometric series that represents 0.4444... as a fraction is: 4/6 * [k=0, ∞]∑1/6^k