Line having power nine

Let $\mathcal I=\displaystyle{ \sum_{r=1}^\infty \dfrac{1 }{r^9}}$ and $\displaystyle\mathcal S={ \sum_{r=1}^\infty \dfrac{1}{ (2r-1)^9}}$

Then the equation of given line can be written in the form: $y=\color{#3D99F6}{\dfrac{512~\mathcal S}{511~\mathcal I}}x$

Now, $\mathcal{I}=\displaystyle{ \sum_{r=1}^\infty \dfrac{1 }{r^9}} = \underbrace{\displaystyle{ \sum_{r=1}^\infty \dfrac{1}{ (2r-1)^9}}}_{\large\mathcal S}+\underbrace{\displaystyle{ \sum_{r=1}^\infty \frac{1 }{(2r)^9}}}_{\large\frac{1}{2^9}(\mathcal{I})=\frac{\mathcal I}{512}}$ $\large\implies \dfrac{511~\mathcal I}{512}=\mathcal{ S}$

$\large \implies \color{#3D99F6}{\dfrac{512~\mathcal S}{511~\mathcal I}}=\huge\boxed{\color{#D61F06}{1}}$

(which is obviously the slope of given line)