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Could someone please check my work and K70 Prove : If lim sup ( s.) = too, then lim sup ( K. S, ) =

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Could someone please check my work

image text in transcribed
and K70 Prove : If lim sup ( s.) = too, then lim sup ( K. S, ) = to Theorem 4.4.8 States that every unbounded sequence ConTats a monotone subsequence That has either top or - as a limit. Suppose lim sup (Sn) = to. - By Theorem 4.4.8, There exists a subsequence of (S.) That has too as a limit. This implies that (s. ) is unbounded above. Thus for every MER There exists a natural number in such That SAM. Then since KYO. Kan > K.M. Then ( K. Sn) is unbounded above. There fore, lim sup ( K. S. ) = + 4

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