MthT 430 Problem Set 02
MthT 430 Problem Set 02
In class September 5, 2007 - Turn in September 12, 2007
Group Work Rules:
•
You are encouraged to work together!
•
Away from the group, do your own neat write up of the problems.
•
Acknowledge the group members and any other person/source you use.
This assignment should be typed or written very neatly.
In writing a proof using mathematical induction (PMI), write a careful statement of P(k).
1.
Prove by PMI or otherwise:
1
3
+ 2
3
+ …+ n
3
= (1 + 2 + …+ n)
2
.
This also proves a formula stated in Spivak Problem 2.7.
See also
http://www.math.com/tables/expansion/power.htm
2.
(Spivak Problem 2.19) Prove the inequality (Bernoulli): If h > −1, then
(1 + h)
n
≥ 1 + n h.
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On 22 Aug 2014, 12:59.