Stepwise problems - Thu. 11:59pm
Sequences
01
01
Link to originalL’Hopital practice - converting indeterminate form
By imitating the technique of the L’Hopital’s Rule example, find the limit of the sequence:
Solution
02
05
Link to originalLimits and convergence
For each sequence, either write the limit value (if it converges), or write ‘diverges’.
(a)
(b) (c) (d)
(e)
Solution
Series
03
01
Link to originalGeneral term of a series
Write this series in summation notation:
(Hint: Find a formula for the general term
.)
Solution
Regular problems - Next Wed. 11:59pm
Sequences
04
03
Link to originalComputing the terms of a sequence
Calculate the first four terms of each sequence from the given general term, starting at
: (a)
(b) (c) (d) (e) (f)
Solution
05
04
Link to originalGeneral term of a sequence
Find a formula for the general term (the
term) of each sequence: (a)
(b) (c)
Solution
06
02
Link to originalSqueeze theorem
Determine whether the sequence converges, and if it does, find its limit:
(a)
(b) (Hint for (b): Verify that
.)
Solution
Series
07
05
Link to originalSeries from its partial sums
Suppose we know that the partial sums
of a series are given by the formula . (a) Compute
. (b) Find a formula for the general term
. (c) Find the sum
.
Solution
08
06
Link to originalGeometric series - partial sums and total sum
Consider the series:
(a) Compute a formula for the
partial sum . (You may apply the known formula or derive it again in this case using the “shift method.”) (b) By taking the limit of this formula as
, find the value of the series. (c) Find the same value of the series by computing
and and plugging into .
Solution