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Determine Whether the Series Is Convergent or Divergent by Expressing SnS _ { n }

Question 109

Short Answer

Determine whether the series is convergent or divergent by expressing SnS _ { n } as a telescoping sum. If it is convergent, find its sum.
∑n=2∞5n(n2−1)\sum _ { n = 2 } ^ { \infty } \frac { 5 } { n \left( n ^ { 2 } - 1 \right) }

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