Question

Determine whether the sequence with the nth term is monotonic and whether it is bounded: a_n =4-(1/n)

Answer 1

I can prove it is monotonic but am somewhat confused on how to prove it is bounded.

Answer 2

well, for large n, this converges to 4 so its bounded

whats the definition of monotonic again?

Answer 3

Monotonic means it is non decreasing or non increasing. How do you show the work to prove it is bounded or not? The monotonic part I am ok with. It is showing that it is bounded that is giving me the hard time

Answer 4

take the limit as n to infinity i believe

Answer 5

lim 4-1/n

lim 4 - lim 1/n

4 - 0 = 4

Answer 6

If it is bounded I have to show algebraically what it is bounded by. It is almost like the squeeze theorem. If you have a second I can show you how my professor did it on one example, but I am slow with the equation thing so It might take me five or ten minutes.

Answer 7

There is a theorem that says if a sequence is bounded and monotonic then it converges. I have to use that to prove the sequence converges

Answer 8

do you have to use a squeeze play on it?

Answer 9

It is similar but very different in the proof

Answer 10

4-1/n = (4n-1)/n

0<1/n<1

0>-1/n>-1

4>4-1/n>4-1

Answer 11

that seems reasonable do you always just deal with the function and then build from that?

Answer 12

thats the way ive seen the squeeze thrm work out yes; start with the basic function and build from there

Answer 13

You know I just checked the answer and it gives a sub n is greater than or equal to three and it doesn't give the other bound.

Answer 14

yes 3 > an > 4 :)

Answer 15

blahahaha that was terrible I just saw the one. Thanks

Answer 16

not sure why its not giving out the 4

Answer 17

:) youre welcome

Answer 18

Because text book publishers make as many mistakes as I do