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

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

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

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

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

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

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

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

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

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

mukushla Group TitleBest ResponseYou've already chosen the best response.0
*increases
 2 years ago

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

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

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

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

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

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

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

malevolence19 Group TitleBest 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.
 2 years ago

malevolence19 Group TitleBest ResponseYou've already chosen the best response.0
it does not*
 2 years ago

malevolence19 Group TitleBest ResponseYou've already chosen the best response.0
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.
 2 years ago
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