GATE | GATE CS 2013 | Question 61

Find the sum of the expression

(A) 7
(B) 8
(C) 9
(D) 10


Answer: (B)

Explanation: The Series can be re-written as

(√2-√1)/(√2+√1)(√2-√1) + (√3-√2)/(√2+√2)(√3-√2) + ……….

which simplifies to

(√2-√1) + (√3-√2) + ….. (√81-√80)

which again simplifies to
√81 – √1

which is 8

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