MthT 430 Chapter 2 Projects to Turn in September 20, 2006

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:

13 + 23 + ¼+ n3 = (1 + 2 + ¼+ 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 ³ 1 + n h.

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