### Big, Bigger, Biggest

Which is the biggest and which the smallest of $2000^{2002}, 2001^{2001} \text{and } 2002^{2000}$?

### Infinite Continued Fractions

In this article we are going to look at infinite continued fractions - continued fractions that do not terminate.

### Gosh Cosh

Explore the hyperbolic functions sinh and cosh using what you know about the exponential function.

# Equation Attack

##### Age 16 to 18 Challenge Level:

Solve the equation $$a^x + b^x = 1$$ where $0< a, b < 1$ and $a + b < 1$, in the special cases:

(i) $a = b\quad$ (ii) $a = {1\over 2}, \ b={1\over 4}\quad$ (iii) $a = {1\over 2}, \ b={1\over 3}$ .

Although you can find exact solutions in special cases like (i) and (ii) it soon becomes apparent that generally you will need to use a numerical method for finding approximate solutions.