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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