problem

### And so on - and on -and on

Can you find the value of this function involving algebraic
fractions for x=2000?

problem
###
And so on - and on -and on

Can you find the value of this function involving algebraic
fractions for x=2000?

problem
###
Production Equation

Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?

problem
###
Golden Powers

You add 1 to the golden ratio to get its square. How do you find higher powers?

problem
###
Loopy

Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$
for different choices of the first two terms. Make a conjecture
about the behaviour of these sequences. Can you prove your
conjecture?

problem
###
Poly Fibs

A sequence of polynomials starts 0, 1 and each poly is given by
combining the two polys in the sequence just before it. Investigate
and prove results about the roots of the polys.

article
###
Powerful properties

Yatir from Israel wrote this article on numbers that can be written as $ 2^n-n $ where n is a positive integer.