Use the Integral Test and \(n = 8\) to estimate the value of \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{1}{{\,n\,\,{{\left( {\ln n} \right)}^2}}}} \).
Use the Integral Test and \(n = 14\) to estimate the value of \( \displaystyle \sum\limits_{n = 0}^\infty {\frac{1}{{{{\left( {2n + 1} \right)}^{\frac{5}{2}}}}}} \).
Use the Comparison Test and \(n = 10\) to estimate the value of \( \displaystyle \sum\limits_{n = 0}^\infty {\frac{{{3^n} - 2}}{{{2^{2n}} + 1}}} \).
Use the Comparison Test and \(n = 8\) to estimate the value of \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{n^2}}}{{{n^4} + 1}}} \).
Use the Alternating Series Test and \(n = 12\) to estimate the value of \( \displaystyle \sum\limits_{n = 0}^\infty {\frac{{{{\left( { - 1} \right)}^n}}}{{n + 1}}} \).
Use the Alternating Series Test and \(n = 18\) to estimate the value of \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{{\left( { - 1} \right)}^n}\sqrt n }}{{3n + 4}}} \).
Use the Ratio Test and \(n = 10\) to estimate the value of \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{{\left( { - 2} \right)}^{1 + 2n}}}}{{{n^2}\,{7^n}}}} \).
Use the Ratio Test and \(n = 5\) to estimate the value of \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{n}{{\left( {n - 1} \right)!}}} \).