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Question Number 75828 by 21042004 last updated on 18/Dec/19

$$\underset{n=1}{\sum ^{\mathrm{\infty }}}\frac{1}{{10}^n}$$

Commented by mathmax by abdo last updated on 18/Dec/19

$$\sum _{n=1}^{\mathrm{\infty }}\frac{1}{{10}^n}=\sum _{n=0}^{\mathrm{\infty }}{\left(\frac{1}{10}\right)}^n-1=\frac{1}{1-\frac{1}{10}}-1=\frac{10}{9}-1=\frac{1}{9}$$

Answered by MJS last updated on 18/Dec/19

$$=.1+.01+.001+...=.\stackrel{.}{1}=\frac{1}{9}$$

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