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[tex]\mbox {Suppose I have: } \sum_{n=1}^\infty (\frac {x} {3})^{2n} [/tex]
[tex]\mbox{Can I define } y= \frac {x} {3} [/tex]
[tex]
a_k(y) = \left\{
\begin{array}{c l}
(y)^k, & \mbox{if } k= 2n\\
\\
(0)^k, & \mbox{otherwise}
\end{array}
\right.
[/tex]
[tex] \mbox {And then use all the cool properties of power series on } \sum_{k=1}^\infty a_k(y)[/tex]
[I edited my question]
[tex]\mbox{Can I define } y= \frac {x} {3} [/tex]
[tex]
a_k(y) = \left\{
\begin{array}{c l}
(y)^k, & \mbox{if } k= 2n\\
\\
(0)^k, & \mbox{otherwise}
\end{array}
\right.
[/tex]
[tex] \mbox {And then use all the cool properties of power series on } \sum_{k=1}^\infty a_k(y)[/tex]
[I edited my question]
Last edited: