Let s n be a positive sequence such that lim n s n 1s n L 1 Prove thats n Hint

# Let s n be a positive sequence such that lim n s n 1s

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2. Let(sn) be a positive sequence such thatlimn→∞sn+1sn=L >1.Prove thatsn+.Hint:limn→∞xn= +for any numberxsuch thatx >1. 7
3.Limits:Determine the convergence or divergence of each of the followingsequences. If the limit exists, state what it is.(a)sn=n2+ 3n14n53n3+ 2nsn=n2+ 3n14n53n3+ 2nn22n5/2=12n1/20(b)sn=n33nsn+1sn=(n+ 1) (c)sn=n! (d)sn=nnn! 8
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• Fall '08
• Staff
• Mathematical analysis, Limit of a sequence, Limit superior and limit inferior, Sn, subsequence