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[tex]\sum_{n=1}^\infty \frac{2n^4}{n^5+7}[/tex] this diverges using the p-series and comparison test right? p <1

[tex]\sum_{n=1}^\infty \frac{2n^4}{n^9+7}[/tex] and this converges right? because p > 1

[tex]\sum_{n=1}^\infty \frac{-1^n}{9n}[/tex] i think this also diverges cause p <1. (not sure about this one)

can someone check these real quick and tell me if I am correct?