I have [tex]\sum_{n=1}^\infty{\frac{1}{n^2+n+1}}[/tex] and I need to show that it converges or diverges. I choose to do the comparison test making [tex]A_n=\sum_{n=1}^\infty{\frac{1}{n^2+n+1}}[/tex] and[tex] B_n=\sum_{n=1}^{\infty}\frac{1}{n^2+n}[/tex] so far so good? Okay well [tex] \lim_{n\rightarrow0}B_n=0[/tex] so does [tex]A_n[/tex] converge...i see that the upper limit of [tex]A_n[/tex] would turn out to be [tex]0[/tex] what does this mean...is it valid to use the rule I used?(adsbygoogle = window.adsbygoogle || []).push({});

what if did [tex]\int_{1}^{\infty}\frac{1}{x^2+x+1}dx[/tex] is that possible or is there no need?

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# Homework Help: Methods for convergence divergence

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