Question

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+..+\frac{1}{90}\)

Answer 1

\(\Rightarrow A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\)

\(\Rightarrow A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

\(\Rightarrow A=1-\frac{1}{10}\)

\(\Rightarrow A=\frac{9}{10}\)

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Answer 2

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