What is the value of 1/(2 × 3) + 1/(3 × 4) + 1/(4 × 5) + … + 1/(9 × 10)?
Correct answer D. 2/5
Explanation
Each term splits as 1/(n(n + 1)) = 1/n − 1/(n + 1). The terms cancel in pairs, leaving 1/2 − 1/10 = 4/10 = 2/5.
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