## anonymous 5 years ago so here is a question about absolute convergence see if it is right

1. anonymous
2. anonymous

i got it converges over the intervale -3<x<3

3. anonymous

am i doing it right

4. anonymous

does this stem from a previous question? what is the power series?

5. anonymous

the link i posted is the question

6. anonymous
7. anonymous
8. anonymous

okay it was not showing up , one sec I'll take a look

9. anonymous

thanks :) i think i am doing it wrong though

10. anonymous

yeah, i am getting different numbers

11. anonymous

what did you get though

12. anonymous

i have not check the end points yet but I got 8<x<12

13. anonymous

how did you do it though

14. anonymous

I used the ratio test

15. anonymous

that is what i did

16. anonymous

$\frac{(x-5)^{(n+1)}}{(n+1)2^{(n+1)}}\frac{n2^n}{(x-5)^n}$

17. anonymous

simplifying$=(x-5)\frac{n}{2(n+1)}$

18. anonymous

and $lim_{n\rightarrow\infty}(x-5)\frac{n}{2(n+1)}$$=(x-5)\frac{1}{2}$

19. anonymous

wait a minute

20. anonymous

yes that is what I got

21. anonymous

you are right

22. anonymous

oh

23. anonymous

sorry 3<x<7

24. anonymous

oh how

25. anonymous

$-1<\frac{1}{2}(x-5)<1$

26. anonymous

so$-2<x-5<2$

27. anonymous

ah i see

28. anonymous

adding 5$3<x<7$

29. anonymous

oh ok

30. anonymous

it does not converge absolutely at x=3

31. anonymous

although it does converge at x=3, just not absolutely

32. anonymous

it does not converge at all at x=7

33. anonymous

hmm yes so (3,7) or [3.7)

34. anonymous

well, it depends it converges absolutely on (3,7) and conditionally at 3

35. anonymous

If the question asks what is the interval of absolute convergence, I would answer (3,7) because clearly the series that arises when x=3 converges conditionally

36. anonymous

by the alternating series test

37. anonymous

okay just looked at the question again My answer would be : converges absolutely on (3,7), conditionally at x=3 and diverges at x=7

38. anonymous

hmm yes so (3,7) or [3.7)

39. anonymous

The question asked "for what values of x does the series, converge absolutely? converge conditionally?, diverge? So you must address all three questions which my answer above does