Exercise 1
Prove that the sequence
has a limit of
. Also, calculate the terms whose distance from
is less than
.
Exercise 2
Prove that the sequence
has a limit of
and calculate how many terms of the succession are not within
.
Exercise 3
Prove that the sequence
has a limit of
and calculate how many terms of the succession are not within
.
Exercise 4
Prove that
. Also, calculate the terms whose distance from the limit is less than
.
Exercise 5
Prove that the sequence
has a limit of
and determine how many terms in the sequence are less than a million?
Exercise 6
Prove that the sequence
a has a limit of 
. Also, what term of the sequence produces values of less than
?
Solution of exercise 1
Prove that the sequence has a limit of . Also, calculate the terms whose distance from is less than .
From
the distance to
is less than
Solution of exercise 2
Prove that the sequence has a limit of and calculate how many terms of the succession are not within .
The first thousand terms of the sequence are out.
Solution of exercise 3
Prove that the sequence has a limit of and calculate how many terms of the succession are not within .
The first 
terms are out.
Solution of exercise 4
Prove that . Also, calculate the terms whose distance from the limit is less than .
From 
the distance to the limit is less than .
Solution of exercise 5
Prove that the sequence has a limit of and determine how many terms in the sequence are less than a million?
The 
first terms of the sequence.
Solution of exercise 6
Prove that the sequence a has a limit of . Also, what term of the sequence produces values of less than ?
If 
, its square root is 
, therefore, 
a101 will be less than .
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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