## privetek Group Title determine absolute or conditional convergence: sum(k=1 -> infinity) [(-1)^(k+1)(10^k)]/(k!) one year ago one year ago

1. mukushla Group Title

have u tried ratio test?

2. privetek Group Title

well it's an alternating series. i think i'm supposed to use the alternating series test

3. mukushla Group Title

of course alternating series test will work :)

4. privetek Group Title

i'm not sure how i'm supposed to do it because of the k+1 on the -1

5. mukushla Group Title

u just need to drop $(-1)^{k+1}$and then work on$\frac{10^k}{k!}$

6. mukushla Group Title

this is a good sourse http://tutorial.math.lamar.edu/Classes/CalcII/AlternatingSeries.aspx

7. mukushla Group Title

what is ur difficulty with that??

8. privetek Group Title

ok.. now i get that.. so how should i take the limit of 10^k/k! ?

9. mukushla Group Title

oh sorry i was out ;) well k! is very greater than 10^k when k increses

10. mukushla Group Title

*increases

11. privetek Group Title

so would that mean that the limit would go to zero?

12. mukushla Group Title

yes

13. privetek Group Title

how to tell weather it converges absolutely or conditionally?

14. mukushla Group Title

emm...u should apply Absolute Convergence test

15. privetek Group Title

sorry.. i kinda don't understand how to do that here... could you help me out??

16. mukushla Group Title

ok u got the first part right? alternating series test?

17. privetek Group Title

yes, lim(k>infinity)[10^k/k!] = 0

18. privetek Group Title

therefore it converges

19. privetek Group Title

@mukushla

20. malevolence19 Group Title

$\lim_{k \rightarrow \infty}a_k=0$ Is a REQUIREMENT for a series to converge but it doesn't not IMPLY that a series converges.

21. malevolence19 Group Title

it does not*

22. malevolence19 Group Title

Even if it is an alternating series do the ratio test, the ratio test works well for factorials. Also, if that converges then you know it absolutely converges (because you take the absolute value so the (-1)^k+1 goes away) and if it absolutely converges then you know it conditionally converges.