Period of the decimal expansion of $\frac{1}{9801}$

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I have to show that $\frac{1}{9801}= 0.\overline{000102030405060708\dots9799}$. Here bar denotes Period.

My Attempt: I have shown $\frac{1}{9801}= {0.000102030405060708........9799.........}$ using the power series expansion of $\frac{1}{(1-x)^2}$. But I can not find the period of the decimal expansion of $\frac{1}{9801}$.

Can anyone help me with this ?