I am trying to derive the geometric series for the following given(adsbygoogle = window.adsbygoogle || []).push({});

identities,

[tex]

\begin{array}{l}

\frac{1}{{0.99}} = 1.0101010101... \; \; \; {\rm{ (1)}} \\

[/tex]

[tex]

\frac{1}{{0.98}} = 1.0204081632... \; \; \; {\rm{ (2)}} \\

\end{array}

[/tex]

Here is my answer for (1),

[tex]

\sum\limits_{n = 1}^\infty {\left( {\frac{1}{{100}}} \right)} ^n + 1

[/tex]

Here is my answer for (2),

[tex]

\sum\limits_{n = 1}^\infty {\left( {\frac{1}{{50}}} \right)} ^n + 1

[/tex]

Are my answers correct? The only way I can get the correct answer is by

adding 1 onto the series. Is this the correct way represent the series?

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# Deriving a geometric series

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