lim n→∞ [n/n² + n/n²+1 + n/n²+2 + ... + n/n³+(n-1)] is equal to?
- 0
- n/2
- n/3
- None of these
Explanation
Sₙ = n/(n³+0) + n/(n³+1) + ... + n/(n³+n-1) = Σₖ₌₀ⁿ⁻¹ n/(n³ + k)
Each term ≤ n/n³ = 1/n²
There are n terms → Sₙ ≤ n × 1/n² = 1/n → 0 as n→∞
Lower bound: n/(n³+n-1) × n = n²/(n³+n-1) → 0
By squeeze theorem, limit = 0
Last verified on 05-06-2026
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