The value of \((\frac{1}{\sqrt{9}-\sqrt{8}} - \frac{1}{\sqrt{8}-\sqrt{7}} + \frac{1}{\sqrt{7}-\sqrt{6}} - \frac{1}{\sqrt{6}-\sqrt{5}} + \frac{1}{\sqrt{5}-\sqrt{4}})\) is
Question and options
The value of is
- 0
- 1
- 5
Answer and explanation
Correct answer: D - 5
Rationalise each term: 1/(sqrt(k+1) - sqrt(k)) = sqrt(k+1) + sqrt(k). The sum is (3+sqrt8) - (sqrt8+sqrt7) + (sqrt7+sqrt6) - (sqrt6+sqrt5) + (sqrt5+2). Everything cancels except 3 + 2 = 5.
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