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

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mukushlaBest ResponseYou've already chosen the best response.0
have u tried ratio test?
 one year ago

privetekBest 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
 one year ago

mukushlaBest ResponseYou've already chosen the best response.0
of course alternating series test will work :)
 one year ago

privetekBest 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
 one year ago

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

mukushlaBest ResponseYou've already chosen the best response.0
this is a good sourse http://tutorial.math.lamar.edu/Classes/CalcII/AlternatingSeries.aspx
 one year ago

mukushlaBest ResponseYou've already chosen the best response.0
what is ur difficulty with that??
 one year ago

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

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

privetekBest ResponseYou've already chosen the best response.0
so would that mean that the limit would go to zero?
 one year ago

privetekBest ResponseYou've already chosen the best response.0
how to tell weather it converges absolutely or conditionally?
 one year ago

mukushlaBest ResponseYou've already chosen the best response.0
emm...u should apply Absolute Convergence test
 one year ago

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

mukushlaBest ResponseYou've already chosen the best response.0
ok u got the first part right? alternating series test?
 one year ago

privetekBest ResponseYou've already chosen the best response.0
yes, lim(k>infinity)[10^k/k!] = 0
 one year ago

privetekBest ResponseYou've already chosen the best response.0
therefore it converges
 one year ago

malevolence19Best 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.
 one year ago

malevolence19Best 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.
 one year ago
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