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
\(\frac{4}{10}+\frac{4}{100}+\frac{4}{1000}+........\)
