Chapters
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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