Math 114 – Computer Assignment 2 – due Wednesday, April 10
You may work in groups, but each member must contribute. Groups
should be no larger than four in size.
Directions: Complete the following assignment using Maple software. Maple
may be used either in a campus PC lab (ST 1; Robinson; Johnson Cen-
ter)where it runs as a program in the folder Instructor Apps or on osf1
using graphical access, as in the math computer lab (ST 1, room 220), which
has X-terminals.
This assignment examines series using Maple’s algebraic capability via the
sum command. Your work should be clear, concise, and complete. Make
sure you indicate how answers were obtained by including sufficient Maple
input/output and commentary. Use the sum command to understand how
comparison really works by considering the three sums:
∞
X
n=1
1
n,
∞
X
n=1
1
n2,
∞
X
n=1
1
n2+ 1.
Part 1: According to our theory, the first sum is divergent, comparable to
an integral that yields the ln function as R∞
1
1
xdx. Make the comparison by
using Maple to compute the following discrete sums as floating point numbers
and compare them to each other and to ln(10): (a) sum of the first terms 1
to 10; (b) sum of terms 11 to 100; (c) sum of terms 101 to 1000. Each of
these last two is a right sum, so it is smaller than the integral. Since the
integral is clear, you should compare with the value of the integral, ln(10).
Part 2: According to our theory, the second and third sums are compara-
ble to integrals and to each other in the limit. Use Maple to confirm this by
computing the sum from k= 101 to 1000 and also k= 1001 to 2000 for both
series and also compute corresponding integrals. Compare all the pieces with
each other.
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