- #1
rocomath
- 1,755
- 1
[tex]\sum_{n=1}^{\infty}\frac{(-1)^{n}n}{n^{2}+25}[/tex]
Ratio Test
[tex]\lim_{n\rightarrow\infty}|\frac{(-1)^{n+1}(n+1)(n^{2}+25)}{[(n+1)^{2}+25](-1)^{n}n}|[/tex]
[tex]\lim_{n\rightarrow\infty}|\frac{n^{3}+n^{2}+25n+25}{ n^{3}+2n^{2}+26n}|=1[/tex]
Thus, the Ratio Test is inconclusive. So what should my next step be, or other suggestions? Hmm ...
Thanks!
Ratio Test
[tex]\lim_{n\rightarrow\infty}|\frac{(-1)^{n+1}(n+1)(n^{2}+25)}{[(n+1)^{2}+25](-1)^{n}n}|[/tex]
[tex]\lim_{n\rightarrow\infty}|\frac{n^{3}+n^{2}+25n+25}{ n^{3}+2n^{2}+26n}|=1[/tex]
Thus, the Ratio Test is inconclusive. So what should my next step be, or other suggestions? Hmm ...
Thanks!