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For every integer n 1, the value of 1/(12) + 1/(23) + 1/(34) + + 1/[n(n+1)] is:

1. n/(n+1)
2. 1/(n+1)
3. 1/[n(n+1)]
4. None of these

Correct answer: n/(n+1)

Solution

The series can be simplified using the formula for the sum of fractions, where each term can be rewritten as a difference of two fractions, leading to a telescoping series that ultimately simplifies to n/(n+1).

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