CDS 2024 · PYQ · Infinite Series · medium
What is 3/(1²×2²) + 5/(2²×3²) + 7/(3²×4²) + ... equal to?
- A.1✓ Correct
- B.4
- C.7
- D.9
The nth term is (2n+1)/(n²(n+1)²) = 1/n² - 1/(n+1)². This is a telescoping series: sum = 1/1² - lim 1/(n+1)² = 1 - 0 = 1.
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