Question

Is anyone good with converging/diverging series?

Answer 1

Question #8

Answer 2

I think it is divergent

Answer 3

what @OOOPS said

Answer 4

as \(n\) gets large, well, \(n\) gets large so \(a_n\to \infty\)

Answer 5

Thank you guys for the help!

Answer 6

\[a_1=\frac{(-1)^1}{1}+1=-1+1=0 \\ a_2=\frac{(-1)^2}{2}+2=\frac{1}{2}+2=\frac{5}{2} =2.5\\ a_3=\frac{(-1)^3}{3}+3=\frac{-1}{3}+3=\frac{8}{3}= 2.6666667\\ a_4=\frac{(-1)^4}{4}+4=\frac{1}{4}+4=\frac{17}{4}=4.25 \\ a_5= \frac{(-1)^5}{5}+5=\frac{-1}{5}+5=\frac{24}{5}= 4.8\\ a_6=\frac{(-1)^6}{6}+6=\frac{1}{6}+6=\frac{37}{6}=6.166667\]
....
\[a_{100}=\frac{(-1)^{100}}{100}+100=\frac{1}{100}+100=100+\frac{1}{100} \\ a_{600}=\frac{(-1)^{600}}{600}+600=\frac{1}{600}+600=600+\frac{1}{600}\]
as we see the numbers in the sequence are not getting closer to a specific number

Answer 7

yw

Answer 8

they just keep getting larger and larger as @satellite73 says

Answer 9

larger and larger and larger and ...