What is 1/(9-(1/10)^n) ?

The solution to 1/(9-(1/10)^n) is (10^n)/(9*10^n-1)

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simplify 1/(9-(1/10)^n)

simplify

\frac{1}{9 - ( \frac{1}{10} ) ^{n}}

\frac{1 0 ^{n}}{9 \cdot 1 0 ^{n} - 1}

Solution steps

\frac{1}{9 - ( \frac{1}{10} ) ^{n}}

Simplify

9 - (\frac{1}{10})^{n} : \frac{9 \cdot 1 0 ^{n} - 1}{1 0 ^{n}}

= \frac{1}{\frac{9 \cdot 1 0 ^{n} - 1}{1 0 ^{n}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{1 0 ^{n}}{9 \cdot 1 0 ^{n} - 1}

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