Project ForgeGeneral Aptitude
Quantitative Aptitude
GATE 2013
Hard
Find the sum of the expression
1/(√1+√2) + 1/(√2+√3) + 1/(√3+√4) + ............... + 1/(√80+√81)
- A7
- 8
- C9
- D10
Explanation
Rationalize each term: 1/(√n+√(n+1)) = (√(n+1)-√n) / [(√(n+1)+√n)(√(n+1)-√n)] = √(n+1) - √n, since the denominator becomes (n+1)-n = 1. The sum from n=1 to 80 telescopes: (√2-√1) + (√3-√2) + ... + (√81-√80) = √81 - √1 = 9 - 1 = 8.
Source: GATE ME 2013 (Booklet Code A) (2013)
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