A) 0
B) 1
C) 2
D) 4
Correct Answer: C
Solution :
| [c] \[\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{5}}\] |
| \[+\frac{1}{\sqrt{5}+\sqrt{6}}+\frac{1}{\sqrt{6}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{8}}+\frac{1}{\sqrt{8}+\sqrt{9}}\] |
| \[=\frac{1}{1+\sqrt{2}}\times \frac{\sqrt{2}-1}{\sqrt{2}-1}+\frac{1}{\sqrt{3}+\sqrt{2}}\] |
| \[\times \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}+\frac{1}{\sqrt{4}+\sqrt{3}}\times \frac{\sqrt{4}-\sqrt{3}}{\sqrt{4}-\sqrt{3}}\] |
| \[+....+\frac{1}{\sqrt{9}+\sqrt{8}}\times \frac{\sqrt{9}-\sqrt{8}}{\sqrt{9}-\sqrt{8}}\] |
| \[=\sqrt{2}-1+\sqrt{3}-\sqrt{2}+\sqrt{4}-\sqrt{3}+\sqrt{5}-\sqrt{4}\] |
| \[+....+\sqrt{9}-\sqrt{8}\] |
| \[=\,\,\sqrt{9}-1=3-1=2\] |
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