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i must find lim of a_n for x_n = 1/n( 1/ln(2) + ... + 1/ln(n) ) using stoltz cesaro theorem
 one year ago
 one year ago
i must find lim of a_n for x_n = 1/n( 1/ln(2) + ... + 1/ln(n) ) using stoltz cesaro theorem
 one year ago
 one year ago

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mahmit2012Best ResponseYou've already chosen the best response.0
xn>int 1/xlnx]1 to inf=ln(lnx)]1 to inf=inf so limxn=inf
 one year ago

graydarlBest ResponseYou've already chosen the best response.0
(1/n)*( 1/ln(2) + ... + 1/ln(n) ) is the equation sorry
 one year ago

graydarlBest ResponseYou've already chosen the best response.0
I must use stoltz cesaro \[\frac{a_{n+1}a ^{n} }{ b_{n+1}b ^{n} }\] for \[x _{n}=\frac{ 1 }{ n}*(\frac{ 1 }{ \ln_{2} }+ ... +\frac{ 1 }{ \ln_{n} })\] and i don t know how to find \[a_{n}\] and \[b _{n}\]
 one year ago

cnkndBest ResponseYou've already chosen the best response.1
try b_n = n, and a_n = 1/ln2 + ... + 1/ln(n)
 one year ago

graydarlBest ResponseYou've already chosen the best response.0
with n get lim = 0 which is good but can i take only n and not 1/n as b_n? :D
 one year ago

mahmit2012Best ResponseYou've already chosen the best response.0
I compare with integral which it approach to infinity then I conclude the series is also infinity or it is diverged.
 one year ago

graydarlBest ResponseYou've already chosen the best response.0
i have a hint and says that the result is 0 but if i consider b_n 1/n the result is infinity so i don't know if the hint is good or not or whick one is correct
 one year ago

cnkndBest ResponseYou've already chosen the best response.1
ugh you want x_n in the form of a_n/b_n... so tell me, what would a_n be if b_n = 1/n?
 one year ago

graydarlBest ResponseYou've already chosen the best response.0
you' re right now i saw that if u write them your way is the same thing, is correct, i understood and the result is 0 as it should be thank you very muc :D i apreciate it
 one year ago
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