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Answer: It can be expressed as
[tex]\frac{4}{10}+\frac{4}{100}+\frac{4}{1000}+........[/tex]
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,
[tex]\frac{4}{10}+\frac{4}{100}+\frac{4}{1000}+\frac{4}{10000}............[/tex]
and it is a geometric series.
Because it has first term = a = [tex]\frac{4}{10}[/tex]
and common ratio = r = [tex]\frac{a_2}{a_1}=\frac{\frac{4}{100}}{\frac{4}{10}}=\frac{1}{10}[/tex]
Hence, it can be expressed as
[tex]\frac{4}{10}+\frac{4}{100}+\frac{4}{1000}+........[/tex]