What is the value of 1/(1 + √2) + 1/(√2 + √3) + 1/(√3 + √4) + … + 1/(√15 + √16)?
Correct answer A. 3
Explanation
Rationalising, 1/(√n + √(n + 1)) = √(n + 1) − √n. The sum telescopes to √16 − √1 = 4 − 1 = 3.
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