Unbounded Sequence (bn): Convergence of Subsequence (b(kn))

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The discussion centers on the mathematical concept of an unbounded sequence (bn) and its subsequence (b(kn)). It is established that if (bn) is unbounded, then there exists a subsequence (b(kn)) such that the limit of the reciprocal of (b(kn)) approaches zero, expressed as lim (1/(b(kn))) = 0. This conclusion is critical for understanding the behavior of unbounded sequences in mathematical analysis.

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If (bn) is an unbounded sequence then it has a sequence (b(kn)) such that lim (1/(b(kn)))=0

(where kn is a subsequence of bn )
 
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Welcome to PF!

Hi gankutsuou! Welcome to PF! :smile:

(try using the X2 tag just above the Reply box :wink:)

Do the obvious …

start "If {bn} is unbounded, then for any n … " :smile:​
 

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