Limit of Sequence Problems

Solutions

1Prove that the sequence has a limit of 2. Also, calculate the terms whose distance from 2 is less than 0.1.

2Prove that the sequence has a limit of 4 and calculate how many terms of the succession are not within (4 − 0.001, 4 + 0.001).

3Prove that the sequence has a limit of 1 and calculate how many terms of the succession are not within (1 − 0.001, 1 + 0.001).

4Prove that Limit of a Sequence. Also, calculate the terms whose distance from the limit is less than 0.01.

5Prove that the sequence has a limit of +∞ and determine how many terms in the sequence are less than a million?

6Prove that the sequence an= −n2 has a limit of −∞. Also, what term of the sequence produces values of less than −10,000?


1

Prove that the sequence has a limit of 2. Also, calculate the terms whose distance from 2 is less than 0.1.

Defining the Limit

Defining the Limit

Defining the Limit

Froma41 the distance to 2 is less than 0.1.


2

Prove that the sequence has a limit of 4 and calculate how many terms of the succession are not within (4 − 0.001, 4 + 0.001).

Defining the Limit

Defining the Limit

Defining the Limit

The first thousand terms of the sequence are out.


3

Prove that the sequence has a limit of 1 and calculate how many terms of the succession are not within (1 − 0.001, 1 + 0.001).

Defining the Limit

Defining the Limit

Defining the Limit

Defining the Limit

The first 54 terms are out.


4

Prove that Limit of a Sequence. Also, calculate the terms whose distance from the limit is less than 0.01.

Defining the Limit

Defining the Limit

Defining the Limit

Defining the Limit

From a219 the distance to the limit is less than 0.01.


5

Prove that the sequence has a limit of +∞ and determine how many terms in the sequence are less than a million?

The 1,999 first terms of the sequence.


6

Prove that the sequence an= −n2 has a limit of −∞. Also, what term of the sequence produces values of less than −10,000?

−1, −4, −9, −16, −25, −36, −49, ...

Limit of Infinity

If N = 10,000, its square root is 100, therefore, a101 will be less than −10,000.

a101= −1012 = −10,201