What is the value of 1/ {1 +\sqrt 2 }+1/{\sqrt2+\sqrt 3} +...+1/{\sqrt15 +\sqrt16 }?

RRB NTPC Mains or Stage 2 Model Paper 5 with solutions

Question : 15 of 120

Marks: +1, -0

What is the value of

1/ {1 +√ 2 }+1/{√2+√ 3} +...+1/{√15 +√16 }

Solution:

(d)

1/ {1 +√2}+1/{√2 +√3 }+..+1/{√15+√ 16}

(on rationalisation)

= {1- √2}/{1- 2} +{√2-√3} /{2-3}+...+{√ 15 -√16}/{ 15 -16}

= -1(1- √2 + √2 -√ 3 + ... + √15 - √16 )

= -1(1- 4) = 3

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