prove 14 Suppose that lim sn s with s 0 Prove that there e

Suppose that lim s_n = s, with s > 0. Prove that there exists N elementof N such that s_n > 0 for all n greaterthanorequalto N. Prove that x is an accumulation point of a set S iff there exists a

Solution

14. Choose: 0<e<s

Since lim sn=s

So there exis N so that for all n>=N

|sn-s|<e

-e<sn-s<e

s-e<sn<s+e

s>e so s-e>0

Hence, sn>s-e>0

ie sn>0 for all n>=N

Hence proved