- #1
opticaltempest
- 135
- 0
I am trying to derive the geometric series for the following given
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?
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?