Let $$S_n=\sum_{k=1}^n\frac{n}{n^2+kn+k^2}$$ and $$T_n=\sum_{k=1}^n\frac{n-1}{n^2+kn+k^2} $$ for $n=1,2,3$. Then
- $S_n < π /3\sqrt{3}$
- $S_n > π/3\sqrt{3}$
- $T_n < π/3\sqrt{3}$
- $T_n> π/3\sqrt{3}$
Problem on convergence of series with constraints
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sequences-and-series
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0See here for learning about MathJax: http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – 2017-01-24