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privetek
 2 years ago
determine absolute or conditional convergence:
sum(k=1 > infinity) [(1)^(k+1)(10^k)]/(k!)
privetek
 2 years ago
determine absolute or conditional convergence: sum(k=1 > infinity) [(1)^(k+1)(10^k)]/(k!)

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mukushla
 2 years ago
Best ResponseYou've already chosen the best response.0have u tried ratio test?

privetek
 2 years ago
Best ResponseYou've already chosen the best response.0well it's an alternating series. i think i'm supposed to use the alternating series test

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.0of course alternating series test will work :)

privetek
 2 years ago
Best ResponseYou've already chosen the best response.0i'm not sure how i'm supposed to do it because of the k+1 on the 1

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.0u just need to drop \[(1)^{k+1}\]and then work on\[\frac{10^k}{k!}\]

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.0this is a good sourse http://tutorial.math.lamar.edu/Classes/CalcII/AlternatingSeries.aspx

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.0what is ur difficulty with that??

privetek
 2 years ago
Best ResponseYou've already chosen the best response.0ok.. now i get that.. so how should i take the limit of 10^k/k! ?

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.0oh sorry i was out ;) well k! is very greater than 10^k when k increses

privetek
 2 years ago
Best ResponseYou've already chosen the best response.0so would that mean that the limit would go to zero?

privetek
 2 years ago
Best ResponseYou've already chosen the best response.0how to tell weather it converges absolutely or conditionally?

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.0emm...u should apply Absolute Convergence test

privetek
 2 years ago
Best ResponseYou've already chosen the best response.0sorry.. i kinda don't understand how to do that here... could you help me out??

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.0ok u got the first part right? alternating series test?

privetek
 2 years ago
Best ResponseYou've already chosen the best response.0yes, lim(k>infinity)[10^k/k!] = 0

privetek
 2 years ago
Best ResponseYou've already chosen the best response.0therefore it converges

malevolence19
 2 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{k \rightarrow \infty}a_k=0\] Is a REQUIREMENT for a series to converge but it doesn't not IMPLY that a series converges.

malevolence19
 2 years ago
Best ResponseYou've already chosen the best response.0Even 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.
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