What is the value of 5/{\sqrt2+1} + 5/ {\sqrt3+ \sqrt2} + 5/{\sqrt 4+\sqrt 3 } +.... 5 /{\sqrt121+ \sqrt120} ?

SSC CHSL 4 Mar 2018 Shift 3 Paper

Section: English Language

Question : 14 of 100

Marks: +1, -0

What is the value of

5/{√2+1} + 5/ {√3+ √2} + 5/{√ 4+√ 3 }

+.... 5 /{√121+ √120}

Solution:

Expression :

5/{√2+1} + 5/ {√3+ √2} + 5/{√ 4+√ 3 }

+.... 5 /{√121+ √120}

Rationalizing the denominator, we get :
=

(5/{√2+1} ×{√2-1}/{√2-1})+(5/ {√3+ √2} ×{√3-2}/{√3-2})

+(5/{√ 4+√ 3 }×{√ 4-√ 3 }/{√ 4-√ 3 })

+....+(5 /{√121+ √120}×{√121- √120}/{√121- √120})

Using,

(a − b)(a + b) = a^ 2 − b ^2

{5×( √2−1)}/(2−1)+{5×( √3− √2)}/(3−2)

+{5×( √4− √3)}/(4−3)

+.... +5×( √121− √120)/ (121−120)

Thus, after cancelling the positive and negative terms alternatively, we are left with :
=

−5 + 5( √121) = −5 + 55 = 50

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