For number 1, consider the sequence and what does that tell you about choice C
Your answer to 5 is not consistent with your answer to 2
hello,
I have (at least I think) learned and understand a lot of definitions and theorems with numerical series and sequences, so i found something like quiz with true and false questions but i don't have the answers from this questions so i need someone to check did i answered them correctly so I can check myself and my understanding of these part of my study
1. which are correct ?
a) every convergent sequence is bounded and monotonous
b) every bounded and monotonous sequence is convergent
c) every bounded sequence have finite or infinite limit
d) if sequence have accumulation point than he is convergent
my answers are b) and c). I think a) is false because if a_n = 1 than it's convergent and it's bounded but not monotonous (or am I wrong), and i think d) is false too because sequence have more than one accumulation point than it can't be convergent (and it didn't say that is just one... it says that sequence have...)
2. which are correct ?
a) every convergent sequence is bounded
b) every convergent sequence is bounded and monotonous
c) if sequence is not bounded than it's not convergent
d) convergent sequence can have more different accumulation points
my answers are a) and c)
3. which are correct ?
a) every non-monotonous sequence is not convergent
b) every monotonous sequence have finite or infinite limit
c) every bounded sequence have at least one accumulation point
d) every divergent sequence is non-monotonous
my answers b) and c)
4. which are correct ?
a) every bounded sequence is convergent
b) every non bounded sequence is divergent
c) every bounded sequence have at least one accumulation point
d) every convergent sequence is monotonous
my answers b) and c)
question no. 5 should not even be there... my mistake while retyping and copy paste
hmmm... if that sequence than limit goes to something like e^(2i) on the interval (0, pi) .... but if i look at that one than even my answer b) is wrong because that sequence is bounded and monotonous but not convergent ?!