Question

in sequence can we think the bound values as limits if we consider that sequence as function?

Answer 1

I'm pretty sure you can. What do you mean by bound values?

Answer 2

upper bound and lower bound

Answer 3

http://tutorial.math.lamar.edu/Classes/CalcII/MoreSequences.aspx

Answer 4

btw hi @ king

Answer 5

Then you can't always consider the bounds as limits. Take for example the sequence \[(-1)^n \]from 0 to infinity. It has clear bounds of \(\pm 1\), but it doesn't have a limit.

In essence, it has to also converge to that bound to be considered a limit.

Answer 6

what if we consider this sequence as a function

Answer 7

Since it's alternating between two fixed values, it doesn't matter if we consider it as a function. It won't ever converge, and you can't consider it as a limit.

Answer 8

okkkkkkkkkkk

Answer 9

I am trying to understand this bound values but it's going over my head although I have tried so much of google as well, can you please explain it to me that what exactly are these thing ?

Answer 10

An upper bound value is basically a value for which all values of the sequence are below it. A lower bound value is a value for which all values of the sequence are above it.

Answer 11

So if you have an upper bound of 5, then all values given by the sequence are less than 5. It's possible that all the values are actually below 4 also, but 5 is still an upper bound.

Answer 12

OK that's very well then how do we determine these value for instance in seq {n/n+1} from n=1 to inf the lower bound value should be 1/2 but in text it says that it's 0

Answer 13

5 is best bound or we can call it unique bound that is more precise

Answer 14

is it?

Answer 15

Are you sure it isn't from 0 to infinity? That would make the best lower bound 0. Otherwise the best lower bound would be 1/2.

Answer 16

no

Answer 17

http://tutorial.math.lamar.edu/Classes/CalcII/MoreSequences.aspx
example 2 (a) The sequence is therefore bounded below by zero

Answer 18

They say it's bound by 0 because all they say is that it's positive. Since any number greater than 0 is positive, it's bounded by 0.

Answer 19

so this statement doesn't mean that the lower bound is 0

Answer 20

then what does it mean that bounded by 0?

Answer 21

A sequence can have multiple bounds. In this case, their explanation only showed that it was greater than 0. It's not the best bound you can have, but it is a bound for the sequence simply because every value is greater than 0.

Answer 22

so the lower bound value is 0 and it doesn't have the upper bound?

Answer 23

sorry the lower bound value is 1/2
what does mean that it is bounded by 0 and 1

Answer 24

As explained by the page, it converges to 1, and the sequence is always less than 1, so it must be bounded by 1 from above (AKA the upper bound is 1). Since they also gave a lower bound of 0, it must mean that the sequence is bounded by 0 and 1.

Answer 25

bravo got it

Answer 26

thanksssssssss

Answer 27

you're welcome.