2022 · Q24
What is (1)/(1 + √2) + (1)/(√2 + √3) + (1)/(√3 + √4) +... + (1)/(√2020 + √2021) equal to?
Elementary MathematicsAlgebra
- A√2020 + 1
- B√2021 + 1
- C√2020 + √2021 - 1
- D√2021 - 1
Explanation
Rationalising, 1/(√k+√(k+1)) = √(k+1)-√k. The sum telescopes: (√2-√1)+(√3-√2)+...+(√2021-√2020) = √2021-1. Hence the keyed option is D.