Please show work If your answer is \"Tine. \" justify by quoting a definition or
ID: 2944824 • Letter: P
Question
Please show work
If your answer is "Tine. " justify by quoting a definition or theorem, or by giving a proof. If your answer is "False. " give a counter - example. If 0, then given any positive number there corresponds a positive integer N such that for all n > N. If for each positive number there is a positive integer N such that sn N, then rightarrow 0. If the sequence (sn) has the property that to each > 0 there corresponds a positive integer n such that |sn - , s| 0 for all then n, then s > 0.Explanation / Answer
a) False
From the definition of limit, sn --> 0 if |sn - 0| < for all n > N.
b) False
sn < 0 --> sn can have a very large negative value. Thus sn doesn't approach infinity neccessarily.
c) False
There must be a positive integer N, such that for ALL n > N : |sn - s| <
d) False
Consider the sequence sn = 1/n. for all values of n, 1/n > 0 but sn --> 0.