मात्रात्मक योग्यता प्रश्न 501
प्रश्न: $ \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}+7}+\frac{1}{\sqrt{7}+\sqrt{8}}+\frac{1}{\sqrt{8}+\sqrt{9}} $ का मान है
विकल्प:
A) 0
B) 1
C) 2
D) 4
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उत्तर:
सही उत्तर: C
हल:
- [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 $
BETA
