Question

A= 1/3.5 + 1/5.7 + 1/7.9 + 1/9.11 +...+1/99.101

Answer 1

\(A=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{99.101}\)

\(\Rightarrow2A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}...+\frac{2}{99.101}\)

\(\Rightarrow2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\)

\(\Rightarrow2A=\frac{1}{3}-\frac{1}{101}\)

\(\Rightarrow2A=\frac{101}{303}-\frac{3}{303}\)

\(\Rightarrow2A=\frac{98}{303}\)

\(\Rightarrow A=\frac{98}{303}:2=\frac{98}{303.2}=\frac{98}{606}=\frac{49}{303}\)

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