0.10110111011110... is irrational.

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How can I prove that this number is irrational?

I wrote it like this, but I don't know if it's right.

$$\frac{100}{9} \sum_{m=1}^\infty \frac{10^m - 1}{10^{(m + 1)(m + 2)/2}} =0.10110111011110...$$