The sum of the expression 1/{\sqrt1+\sqrt2} + 1/{\sqrt2+\sqrt3} + 1/{\sqrt3+\sqrt5} + ... + 1/\sqrt{80}+\sqrt{81} is ;

NIMCET 2016 Question Paper with solutions

Question : 76 of 120

Marks: +1, -0

The sum of the expression

1/{√1+√2}

1/{√2+√3}

1/{√3+√5}

+ ... +

1/{√{80}+√{81}}

is ;

Solution:

Let

S=1/{√1+√2}+1/{√2+√3}+1/{√3+√4}+..+1/{√80-√81}

Applying rationalization rule in each term, we get

S={√2-√1}/{2-1}+{√3-√2}/{3-2}+...+{√81-√80}/{81-80}

=√2-1+√3-√2+...+√81-√80

=9-1=8

Go to Question:

Prev Question

Next Question