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Section 4-13 : Estimating the Value of a Series

  1. Use the Integral Test and \(n = 10\) to estimate the value of \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{n}{{{{\left( {{n^2} + 1} \right)}^2}}}} \). Solution
  2. Use the Comparison Test and \(n = 20\) to estimate the value of \( \displaystyle \sum\limits_{n = 3}^\infty {\frac{1}{{{n^3}\ln \left( n \right)}}} \). Solution
  3. Use the Alternating Series Test and \(n = 16\) to estimate the value of \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{{{{\left( { - 1} \right)}^n}n}}{{{n^2} + 1}}} \). Solution
  4. Use the Ratio Test and \(n = 8\) to estimate the value of \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{3^{1 + n}}}}{{n\,{2^{3 + 2n}}}}} \). Solution