If you have a repeating decimal such as 0.45454545.... and the question was asking for it to be expressed as an infinite series and find the sum of the series, would it be correct to approach it like this:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] 0.45454545... = \frac {45}{100}+ \frac{45}{10000} + \frac{45}{1000000}....[/tex]

so [tex] a=\frac{45}{100} [/tex] and [tex] r=\frac {1}{100} or 0.01 [/tex]

then using [tex] S_\infty= \frac {a}{1-r} [/tex]

i get: [tex] = \frac {45/100} {1-0.01} = \frac {5}{11} [/tex]

I think this is right but I'm not sure....any thoughts? Please and thank you.

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# Infinite Series

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