Question

\(\frac{1}{2.3}+\frac{1}{4.5}+\frac{1}{6.7}+...+\frac{1}{48.49}\)

Answer 1

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{48}-\frac{1}{49}\)

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Answer 2

\(\frac{1}{2\cdot3}+\frac{1}{4\cdot5}+\frac{1}{6\cdot7}+...+\frac{1}{48\cdot49}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{48}-\frac{1}{49}\)

\(=\frac{1}{2}-\frac{1}{49}\)

\(=\frac{47}{98}\)