The value of {1}/{1+\sqrt{2}+ {1}/\sqrt{2}+\sqrt{3}+ {1}/\sqrt{3}+\sqrt{4}+ {1}/\sqrt{4}+\sqrt{5}+ {1}/\sqrt{5}+\sqrt{6}+ {1}/\sqrt{6}+\sqrt{7}+{1}/\sqrt{7}+\sqrt{8}+ {1}/\sqrt{8}+\sqrt{9} is

SSC CGL Tier II 12 Apr 2015 Paper

Question : 51 of 100

Marks: +1, -0

The value of

{1}/{1+√{2}}+ {1}/{√{2}+√{3}}+ {1}/{√{3}+√{4}}+

{1}/{√{4}+√{5}}+ {1}/{√{5}+√{6}}+ {1}/{√{6}+√{7}}+

{1}/{√{7}+√{8}}+ {1}/{√{8}+√{9}}

Solution:

(1)

{1}/{\√{2}+1}= {√{2}-1}/{(\√{2}+1)(√{2}-1)}

=\ {√{2}-1}/{2-1}=√{2}-1

Similarly,

{1}/{√{3}+√{2}}

= {√{3}-\√{2}}/{(√{3}+√{2)}(√{3}-√{2})}

= {√{3}-√{2}}/{3-2}

=√{3}-√{2}

∴ Expression

√{2}-1+√{3}-

√{2}+√{4}-√{3}+√{5}-\√{4}+

√{6}-√{5}+√{7}-√{6}+√{8}-

√{7}+√{9}-√{8}

=√{9}-1

=3-1=2

Go to Question:

Prev Question

Next Question