Mathematics
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OpenStudy (anonymous):
Sequence questions !
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OpenStudy (anonymous):
sequence an= 5n + 1/n
OpenStudy (anonymous):
1) Is it increasing, decreasing, or neither
OpenStudy (anonymous):
( the sequence)
OpenStudy (anonymous):
2) Is the sequence bounded or not bounded?
OpenStudy (anonymous):
\[\huge a_n=5n+\frac{1}{n}\]?
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OpenStudy (anonymous):
yessir
OpenStudy (anonymous):
Increasing for the first
OpenStudy (anonymous):
or
\[\huge a_n=\frac{5n+1}{n}\]?
OpenStudy (anonymous):
the first equation, sorry for the confusion
OpenStudy (misty1212):
HI!!
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OpenStudy (anonymous):
hello :D
OpenStudy (misty1212):
it is definitely increasing right?
OpenStudy (misty1212):
\(5n\) gets bigger and bigger for sure
OpenStudy (anonymous):
yes madam
OpenStudy (misty1212):
and although \(\frac{1}{n}\to 0\) the whole thing gets larger and larger
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OpenStudy (anonymous):
So it would be unbounded
OpenStudy (misty1212):
you need a proof besides the fact that it is obvious?
OpenStudy (misty1212):
oh yes, definitely unbounded
OpenStudy (anonymous):
increasing and unbounded. sounds good to me. No I do not ned a proof
OpenStudy (misty1212):
as \(n\to \infty\) you have \(5n\to \infty\)
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OpenStudy (anonymous):
definitely :D
Could you help me on a similar problem?
OpenStudy (misty1212):
sure
OpenStudy (anonymous):
I think I got the right answers but I want to double check
OpenStudy (anonymous):
Same questions but with an= cosn
OpenStudy (misty1212):
if i can i will help
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OpenStudy (anonymous):
1) neither increase or decrease 2) it is bounded
OpenStudy (misty1212):
yes
OpenStudy (anonymous):
sounds great thank you :)
OpenStudy (misty1212):
\[\color\magenta\heartsuit\]