Discussion

Find the value of \(1/(2\times3) + 1/(3\times4) + 1/(4\times5) + ... + 1/(9\times10)\).

Answer: B

This is a telescoping series. Each term can be split using partial fractions: \(1/(n(n+1)) = 1/n - 1/(n+1)\).

The series becomes: \((\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{5}) + ... + (\frac{1}{9} - \frac{1}{10})\).

All the intermediate terms cancel out.

We are left with \(\frac{1}{2} - \frac{1}{10}\).

\(\frac{5-1}{10} = \frac{4}{10} = \frac{2}{5}\).

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