Volume 25

1989

Actuaries may be regarded as highly trained business mathematicians.

Physics and mathematics have interacted with each other in the course of centuries, each enriching the development of the other.

Q.782 Let $S_n = \frac{1}{1^2-\frac{1}{4}} + \frac{1}{2^2 - \frac{1}{4}}+ \frac{1}{3^2 - \frac{1}{4}} + \cdots + \frac{1}{n^2 - \frac{1}{4}}$. Simply this expression, and show that $n$ is large $S_n$ is approximately equal to 2.
Q.773 Prove that $\tan(36^\circ) \times \tan(72^\circ) = \sqrt{5}.$