Two limits
Let ($val7) be an infinite sequence of real numbers. If one has $val41 and $val42 for $val26 , what can be said about its convergence? (You should choose the most pertinent consequence.)
Comparison of sequences
Let ($val7) and ($val8) be two sequences of real numbers where ($val7) converges towards $val9. If one has $val28 , what can be said about the convergence of ($val8)? (You must choose the most pertinent consequence.)
Growth and bound
Let ($val7) be a sequence of real numbers. If ($val7) is $val20, what can be said about its convergence (after its existence)?
Convergence and difference of terms
Let $val8 be a sequence of real numbers. Among the following assertions, which are true, which are false? - If $val8 $val19, then $val21.
- If $val21, then $val8 $val20.
Convergence and ratio of terms
Let $val7 be a sequence of real numbers. Among the following assertions, which are true, which are false? - If $val7 $val18, then $val20.
- If $val20, then $val7 $val19.
Epsilon
Let $val7 be a sequence of real numbers. What does the condition $val34 imply on the convergence of $val7? (You must choose the most pertinent consequence.)
Fraction 2 terms
Compute the limit of the sequence (un), where
Fraction 3 terms
Compute the limit of the sequence (un), where
Fraction 3 terms II
Compute the limit of the sequence (un), 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 (un), where
?
Monotony I
Study the growth, sup, inf, min, max of the sequence (un) for n $m_ge $val35, where
. Write $val6 for a value that does not exist, and $val7 or -$val7 for +$m_infty or -$m_infty.
Monotony II
Study the growth, sup, inf, min, max of the sequence (un) for n $m_ge $val36, where
. Write $val6 for a value that does not exist, and $val7 or -$val7 for +$m_infty or -$m_infty.
Powers I
Compute the limit of the sequence (un), where
Powers II
Compute the limit of the sequence (un), 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