2024 · Q8
What is (1)/(√(10)+√9)+(1)/(√(11)+√(10))+(1)/(√(12)+√(11))+…+(1)/(√(196)+√(195)) equal to?
Elementary MathematicsNumber System
- A17
- B14
- C11
- D10
Explanation
Rationalize each term: 1/(√(k+1)+√k) = √(k+1) − √k. The sum telescopes from k=9 to k=195: (√10−√9) + (√11−√10) + … + (√196−√195) = √196 − √9 = 14 − 3 = 11. This is option C.