2021 · Q80
If 1/(1×2) + 1/(2×3) + 1/(3×4) + ⋅⋅⋅ + 1/[n(n+1)] = 99/100, then what is the value of n?
Elementary MathematicsNumber System
- A98
- B99
- C100
- D101
Explanation
Each term telescopes: 1/[n(n+1)] = 1/n − 1/(n+1). The sum is 1 − 1/(n+1) = n/(n+1) = 99/100, so n + 1 = 100 and n = 99. Hence option B.