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Solved problems for the chapter:

Convergent and Divergent Geometric Series

View the theory »

Infinite sequence

1. Near point

2. Infinite sequence limit

2.1. Convergence sequence

2.2. Divergent sequence

2.3. Limit of a sequence

3. Evaluation of limits

3.1. Euler's number

4. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:convergent_and_divergent_geometric_series/4754/

Example 1.

Determine whether the given sequence is convergent:

Example 2.

Determine whether the given sequence is convergent:

Find out and write down the properties (increasing, decreasing, boundedness, convergence) for the given sequence:

Find out and write down the properties (increasing, decreasing, boundedness, divergence) for the given sequence:

Find out and write down the properties (increasing, decreasing, boundedness, convergence) for the given sequence:

Calculate the limit:

Calculate the limit:

Calculate the limit:

Calculate the limit:

Find out and write down the properties (increasing, decreasing, boundedness, divergence) for the given sequence:

14.

Calculate the limit:

15.

Find out which terms of the sequence that have a limit equal to lie in the neighbourhood of .

16.

Calculate the limit:

17.

Find out which terms of the sequence with limit lie inside .

18.

Calculate the limit:

19.

We have a sequence with limit . Find out which terms of the sequence are located outside the neighbourhood .

20.

Calculate the limit:

21.

We have a sequence with the general term . Calculate the limit of the sequence and determine from which term the values of the terms of the sequence differ from the limit by less than ?

22.

Calculate the limit of the sequence:

23.

We have the sequence . Find the general term of the sequence and determine from which term the values of the terms of the sequence differ from the limit by more than ?

24.

Calculate the limit of the sequence:

25.

We have the sequence . Find the general term of the sequence and determine from which term the values of the terms of the sequence differ from the limit by less than ?