Question

9/10- 1/90 - 1/72 - 1/56 - 1/30 - 1/20 - 1/12 - 1/6 -1/2

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Answer 1

\(\frac{9}{10}-\frac{1}{90}-\frac{1}{72}-...-\frac{1}{6}-\frac{1}{2}\)

\(=\frac{9}{10}-\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{72}+\frac{1}{90}\right)\)

\(=\frac{9}{10}-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{8.9}+\frac{1}{9.10}\right)\)

\(=\frac{9}{10}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)

\(=\frac{9}{10}-\left(1-\frac{1}{10}\right)\)

\(=\frac{9}{10}-\frac{9}{10}=0\)

Answer 2

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