problem

Favourite

### Converging Product

In the limit you get the sum of an infinite geometric series. What
about an infinite product (1+x)(1+x^2)(1+x^4)... ?

problem
###
Converging Product

Favourite

In the limit you get the sum of an infinite geometric series. What
about an infinite product (1+x)(1+x^2)(1+x^4)... ?

problem
###
Rain or Shine

Favourite

Predict future weather using the probability that tomorrow is wet
given today is wet and the probability that tomorrow is wet given
that today is dry.

problem
###
There's a limit

Favourite

Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you
notice when successive terms are taken? What happens to the terms
if the fraction goes on indefinitely?

problem
###
Witch of Agnesi

Favourite

Sketch the members of the family of graphs given by y =
a^3/(x^2+a^2) for a=1, 2 and 3.

problem
###
Discrete Trends

Favourite

Find the maximum value of n to the power 1/n and prove that it is a
maximum.

problem
###
Exponential Trend

Favourite

Find all the turning points of y=x^{1/x} for x>0 and decide
whether each is a maximum or minimum. Give a sketch of the graph.

problem
###
Spokes

Favourite

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

problem
###
Resistance

Find the equation from which to calculate the resistance of an
infinite network of resistances.

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
###
Over The Pole

Two places are diametrically opposite each other on the same line of latitude. Compare the distances between them travelling along the line of latitude and travelling over the nearest pole.