How many different numbers smaller than 2.10^8 can be formed using the digits 1 and 2 only ?

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How many different numbers smaller than 2.10^8 can be formed using the digits 1 and 2 only ?

Mathematics
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\(\large \color{black}{\begin{align} & \normalsize \text{ How many different numbers smaller than}\ 2\cdot 10^8 \hspace{.33em}\\~\\ & \normalsize \text{ can be formed using the digits 1 and 2 only} \hspace{.33em}\\~\\ & a.)\ 766 \hspace{.33em}\\~\\ & b.)\ 94 \hspace{.33em}\\~\\ & c.)\ 92 \hspace{.33em}\\~\\ & d.)\ 126 \hspace{.33em}\\~\\ \end{align}}\)
Using two digits, How many 1 digit numbers are possible ? How many 2 digit numbers are possible ? How many 3 digit numbers are possible ? . . . How many 8 digit numbers are possible ?
is this correct \(\large \color{black}{\begin{align} 2^{1}+2^{2}+2^{3}+2^{4}+2^{5}+2^{6}+2^{7}+2^{8}=510\hspace{.33em}\\~\\ \end{align}}\)

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right! Next, look at 9 digit numbers. The left most digit can only be 1. If you fix the left most digit at 1, how many numbers are possible by changing remaining 8 digits ?
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