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Sorry about the title everyone but ive posted numerous threads on series and I had to choose an apropriate title :tongue2:

The problem asks to use the ratio test, and determine for which values of x the test is conclusive-either converging or diverging. Then check those cases where the test is inconclusive by some other means.

here is the the series [tex]\sum_{n=3}^{\infty}\frac{x^n}{n3^n}[/tex]...converge or diverge here is what i did [tex]\frac{a_{n+1}}{a_n}[/tex] and that came out to be [tex]\frac{x^{n+1}}{(n+1)(3^{n+1})}[/tex] multiplie by the [tex]\frac{n3^{n}}{x^{n}}[/tex] and after you cross out similar variables and it comes out to be

[tex]\lim_{x\rightarrow \infty}\frac{xn}{3(n+1)}[/tex]

The problem asks to use the ratio test, and determine for which values of x the test is conclusive-either converging or diverging. Then check those cases where the test is inconclusive by some other means.

here is the the series [tex]\sum_{n=3}^{\infty}\frac{x^n}{n3^n}[/tex]...converge or diverge here is what i did [tex]\frac{a_{n+1}}{a_n}[/tex] and that came out to be [tex]\frac{x^{n+1}}{(n+1)(3^{n+1})}[/tex] multiplie by the [tex]\frac{n3^{n}}{x^{n}}[/tex] and after you cross out similar variables and it comes out to be

[tex]\lim_{x\rightarrow \infty}\frac{xn}{3(n+1)}[/tex]

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