2024 · Q35
What is (3)/(1²× 2²)+(5)/(2²× 3²)+(7)/(3²× 4²) + ... equal to ?
Elementary MathematicsNumber System
- A1
- B4
- C7
- D9
Explanation
Each term (2n+1)/(n²(n+1)²) equals 1/n² − 1/(n+1)², so the series telescopes. The partial sums are 1 − 1/(N+1)². Letting N tend to infinity gives 1, option (a).