March 19, 2021

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

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, ** a _{101}** will be less than .