# Sequence monotonic homework problem help

## Homework Statement

Consider the sequence.

http://www.webassign.net/cgi-bin/symimage.cgi?expr=a_n = 4 n + 1/n

(a) Determine whether the sequence is increasing, decreasing, or not monotonic.

(b) Is the sequence bounded?

## The Attempt at a Solution

I got the answer to a and that is increasing

I am not sure about (b). How do I find that out??

Bounded means, it will reach a point where it will stop increasing more and more quickly. For example, if you had just 1/x^2, it will get smaller and smaller and smaller until the increment is tiny and the sum of the sequence will end up converging to a number.

your sequence is 4n + 1/n ... therefore, as n gets bigger and bigger, what will happen? try it out with increasingly big numbers to see the trend. if it keeps getting bigger faster and faster, then its UNBOUNDED.

Mark44
Mentor

Bounded means, it will reach a point where it will stop increasing more and more quickly. For example, if you had just 1/x^2, it will get smaller and smaller and smaller until the increment is tiny and the sum of the sequence will end up converging to a number.
A sequence {sn} is bounded if there are numbers M and N such that M <= sn <= N for all n = 1, 2, 3, ...

Yes it does keep on increasing. It doesn't stop. But I am not sure if it's faster and faster or not. I know it keeps getting bigger. So it's unbounded? And what about (a) increasing?

Mark44
Mentor

You have an = 4n + 1/n, which has no upper bound. A sequence is increasing if an + 1 >= an for all n >= 1. (Some texts use the phrase strictly increasing if an + 1 > an.)