Interpret the Following Sequences and Describe Them.
Exercise 1
an = 1, 2, 3, 4, 5, ... n.Exercise 2
an = -1, −2,−3, −4, −5, ... −n.Exercise 3
an = 2, 3/2, 4/3, 5/4, ..., n+1/n. Exercise 4
an= 2, −4, 8, −16, 32, ..., (−1)n−1 2n.Exercise 5
Exercise 6
Exercise 7
Exercise 8
Solution of exercise 1
an = 1, 2, 3, 4, 5, ... n
It is increasing.
It is bounded below.
1 is the infimum.
It is not bounded above.
It is divergent.
Solution of exercise 2
an = −1, −2,−3, −4, −5, ... −n
It is decreasing.
It is bounded above.
−1 is the supremum.
It is not bounded below.
It is divergent.
Solution of exercise 3
an = 2, 3/2, 4/3, 5/4, ..., n+1/n
It is decreasing.
It is bounded above
2 is the supremum.
It is bounded below.
1 is the infimum.
It is convergent and the limit is 1.
Solution of exercise 4
an= 2, −4, 8, −16, 32, ..., (−1)n−1 2n
It is not monotonous
It is not bounded.
It is neither convergent nor divergent.
Solution of exercise 5
Monotone
3, 4/3, 1, 6/7,...
It is strictly monotonically decreasing.
Limit
a1= 3
a3= 1
a1 000= 0.5012506253127
a1 000 000 = 0.5000012500006
The limit is 0.5.
It is a convergent sequence.
Bounded
As the sequence is decreasing, 3 is an upper bound and the supremum.
0.5 is a lower bound and the infimum.
Thus, the sequence is bounded.
0.5
Solution of exercise 6
2, − 4, 8, −16, ...
It is not monotonous.
It is neither convergent nor divergent.
It is not bounded.
Solution of exercise 7
It is not monotonous.
It is convergent, the limit is 0.
It is bounded above and 1 is the supremum.
It is bounded below and −1 is the infimum.
It is bounded.
−1 ≤a n ≤ 1.
Solution of exercise 8
Monotone
It is strictly monotonically increasing.
Limit
a1= 0.5.
a3= 0.6666 .
a1000= 0.999000999001.
a1000 000 = 0.999999000001.
The limit is 1.
It is a convergent sequence.
Bounded
It is bounded below and 1/2 is the infimum.
It is bounded above and 1 supremum.
The sequence is bounded.
0.5 ≤ a n <1 < p>
Summarise with AI:
Did you like this article? Rate it!
Loading...
I get it somehow, there are others who are unfamiliar and I have a hard time with it but it’s okay that I get it.
Thanks for sharing your thoughts! It’s completely normal to find some parts unfamiliar or more difficult than others. The important thing is that you’re making progress and understanding more as you practise. Keep going! 😊
At least I understood some of it, but there are others that I’m confused about and have a hard time understanding, but I get it.
Thanks for sharing! It’s great that you’ve understood some of it already. Don’t worry if a few parts are still confusing — keep practising and take your time with the trickier sections. You’ll get there! 😊
The lesson was a little difficult for me, especially the word problems, but the examples helped me understand it better.
Thanks for your feedback! Word problems can definitely be tricky, so we’re glad the examples helped make the lesson clearer. Keep practising — it gets easier with time! 😊
Thankyouuu po