- #1
squaremeplz
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Problem Statements
a. if a sequence is montone then every one of its subsequences is monotone.
true.
b. if a sequence is not monotone, then every one of its subsequences is not monotone
false.
c. if a sequence is unbounded, then every one of its susequences is unbounded.
true
d. if a sequene is divergent, then it cannot have a convergent subsequence
false
e. if a sequence tends to +inf, then it cannot have a convergent subsequence
true
f. if a sequence is unbounded, then it cannot have a convergent subsequence
false
g. if lim sup s_n = 0, then lim sup|s_n| = 0
false
h. if kim sup|s_n| = 0, then lim sup s_n = 0
true
i. if lim sup|s_n| = 5, then lim sup s_n = 5
true
j. if lim sup|s_n|= 5, then (s_n) is bounded
false
I actually have to prove out the ones that are true but can someone just let me know if I got the first step right on them. Thanks alot!
a. if a sequence is montone then every one of its subsequences is monotone.
true.
b. if a sequence is not monotone, then every one of its subsequences is not monotone
false.
c. if a sequence is unbounded, then every one of its susequences is unbounded.
true
d. if a sequene is divergent, then it cannot have a convergent subsequence
false
e. if a sequence tends to +inf, then it cannot have a convergent subsequence
true
f. if a sequence is unbounded, then it cannot have a convergent subsequence
false
g. if lim sup s_n = 0, then lim sup|s_n| = 0
false
h. if kim sup|s_n| = 0, then lim sup s_n = 0
true
i. if lim sup|s_n| = 5, then lim sup s_n = 5
true
j. if lim sup|s_n|= 5, then (s_n) is bounded
false
I actually have to prove out the ones that are true but can someone just let me know if I got the first step right on them. Thanks alot!