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OpenStudy (anonymous):
The meaning of the decimal representation of a number\[0.d_1d_2d_3d_4\]where the digit d_i is one of the numbers 0,1,2,...,9 is that \[0.d_1d_2d_3d_4... = \frac{d_1}{10}+\frac{d_2}{10^2}\frac{d_3}{10^3}+\frac{d_4}{10^4}+...\]show that this series always converges
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