#
OEF sequences
--- Introduction ---

This module actually contains 16 exercises on infinite sequences:
convergence, limit, recursive sequences, ...

### Two limits

Let () be an infinite sequence of real numbers. If one has and for , what can be said about its convergence? (You should choose the most pertinent consequence.)

### Comparison of sequences

Let () and () be two sequences of real numbers where () converges towards . If one has , what can be said about the convergence of ()? (You must choose the most pertinent consequence.)

### Growth and bound

Let () be a sequence of real numbers. If () is , what can be said about its convergence (after its existence)?

### Convergence and difference of terms

Let be a sequence of real numbers. Among the following assertions, which are true, which are false? - If , then .
- If , then .

### Convergence and ratio of terms

Let be a sequence of real numbers. Among the following assertions, which are true, which are false? - If , then .
- If , then .

### Epsilon

Let be a sequence of real numbers. What does the condition imply on the convergence of ? (You must choose the most pertinent consequence.)

### Fraction 2 terms

Compute the limit of the sequence (*u*_{n}), where

### Fraction 3 terms

Compute the limit of the sequence (*u*_{n}), where

### Fraction 3 terms II

Compute the limit of the sequence (*u*_{n}), where
**WARNING** IN this exercise, approximative replies will be considered as false! Type `pi` instead of 3.14159265, for example.

### Growth comparison

What is the nature of the sequence (*u*_{n}), where
?

### Monotony I

Study the growth, sup, inf, min, max of the sequence (*u*_{n}) for *n* , where
. Write for a value that does not exist, and or `-` for + or -.

### Monotony II

Study the growth, sup, inf, min, max of the sequence (*u*_{n}) for *n* , where
. Write for a value that does not exist, and or `-` for + or -.

### Powers I

Compute the limit of the sequence (*u*_{n}), where

### Powers II

Compute the limit of the sequence (*u*_{n}), where
Type `no` if the sequence is divergent.

### Recursive function

The sequence
such that
is a recursive sequence defined by
for a certain function
. Find this function.

### Recursive limit

Find the limit of the recursive sequence
such that
Other exercises on:
sequences
Convergence
Limit

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- Description: collection of exercises on infinite sequences. serveur web interactif avec des cours en ligne, des exercices interactifs en sciences et langues pour l'enseigment primaire, secondaire et universitaire, des calculatrices et traceurs en ligne
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