Volume 40
, Issue 1


In the first article in this issue, by Michael Hirschhorn, you will learn about the harmonic series

$$\sum_{k=1}^\infty \frac{1}{k}.$$

If you study series, one of the first divergent series you will meet is the harmonic series,
$$1+\frac12+\frac13+\frac14+\ \cdots\ =\sum_{k=1}^\infty\frac1{k}.$$

Sometime in your senior mathematics course you will have come across arithmetic and geometric sequences.

My first experience with an algebraic manipulation package was about twenty years ago, toward the end of my PhD in theoretical physics.

Q1151. Let $p(x) = (x^{2003} + x^{2002} -1)^{2004}.$  Find the sum of the coefficients of all odd degree terms in the expansion of the trinomial $p(x).$

Q1141. In the 2003 cricket XI there were 7 boys who had been in the 2002 XI, and in the 2002 XI there were 8 boys who had been in the 2001 XI. What is the least number who have been in all three XIs?