BC 2,3
Problem Set #5
(Due Friday, November 1)
Name: ______________
Please show appropriate work – no calculator or computers – except to check work done by hand. Work
should be shown clearly, using correct mathematical notation. Please show enough work on all
problems (unless specified otherwise) so that others could follow your work and do a similar problem
without help. Collaboration is encouraged, but in the end, the work should be your own.

1. Let an be a decreasing sequence of positive numbers. Suppose that the alternating series
 (1) a
n
n0
n
is
conditionally convergent. Now define bn   1 an for n  0 .
n

(a) Show that
b
n0
3n
converges.

(b) Determine whether
b
n0
3n
is conditionally convergent or absolutely convergent? Justify your answer.
BC 2,3
Problem Set #5
(Due Friday, November 1)

2. Find the value of
1
Name: ______________
 k  k ! with an error of at most .0001. Show the error analysis clearly. You may use
k 1
your calculator to do any calculations here, but the analysis should be clear.
BC 2,3
3. Let f (n) 
Problem Set #5
(Due Friday, November 1)

1
. Calculate

n
k 2 k  k !

 f (n)
n2
Name: ______________