monotonic or not?
my teacher was explaining to determine if
4-(1/n) is monotonic you do the following....
(1/n) ? (1/n+1)
(n) ? (n+1)
(n) < (n+1)
0 < 1
ok....so i have this...what does this tell me?
1. what tells me this is monotonic?
2. what tells me this is bounded?
First you have to know what n is. n basically is a "natural" number, meaning from 1,2,3,4...
Now, when n=1, you have 1/n = 1/1 = 1
when n=2, you have 1/2
when n=3, you have 1/3, and so on...
What do you notice? You should that 1/n gets smaller as n gets bigger right?
Now, what does do for 4-1/n? As n gets bigger, what would happen to 4-1/n?
What your teacher is trying do is to get you to understand the relationship between 1/n and 1/(n+1), well, think about it, which one should bigger? That would tie in with above.
Now, monotonic sequence is basically a sequence such that it always decrease, increase, or remain constant as n gets bigger, so what do you think 4-1/n is?
Now, bounded simply implies that a sequence is "bounded" by a certain value, like 1/n itself will decrease, but it will never get as low as 0, in other words, 0 is greater than or equal to 1/n