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(Solved): Determine the sum of the series \\[ \\sum_{n=1}^{\\infty} \\frac{2}{n(n+2)} \\] if possible. (If th ...



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Determine the sum of the series \\[ \\sum_{n=1}^{\\infty} \\frac{2}{n(n+2)} \\] if possible. (If the series diverges, enter 'infinity', '-infinity' or 'dne' as appropriate.) Answer: (Hint: try breaking the summands up partial fractions-style.)


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we have the series   

nth partial sum of the series

  

  
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