Question

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S2 = \(\frac{1}{3.5}+\frac{1}{5.7}+.......+\frac{1}{999.1001}\)

Answer 1

\(S2=\left(\frac{1}{3}-\frac{1}{1001}\right):2=\frac{499}{3003}\)

Answer 2

\(S2=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{999.1001}\)

\(S2=\frac{1}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{999.1001}\right)\)

\(S2=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{999}-\frac{1}{1001}\right)\)

\(S2=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{1001}\right)\)

\(S2=\frac{1}{2}.\frac{998}{3003}=\frac{499}{3003}\)