1. Infinite decimal expansions: We can interpret any finite decimal expansion as a finite sum. For example: [ 2.1309=2+ frac{1}{10}+ frac{3}{10^{2}}+ frac{0}{10^{3}}+ frac{9}{10^{4}} ] Similarly, we can interpret any infinite decimal expansion as an infinite series. Interpret the following numbers as series, and add up the series to calcul solutionspile.com

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1. Infinite decimal expansions: We can interpret any finite decimal expansion as a finite sum. For example:   [ 2.1309=2+  frac{1}{10}+  frac{3}{10^{2}}+  frac{0}{10^{3}}+  frac{9}{10^{4}}   ] Similarly, we can interpret any infinite decimal expansion as an infinite series. Interpret the following numbers as series, and add up the series to calculate their value as fractions: (a)   ( 0.99999   ldots   ) (b)   ( 0.11111   ldots   ) (c)   ( 0.252525   ldots   ) (d)   ( 0.3121212   ldots   ) Hint: use the geometric series formula. solutionspile.com

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