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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)... ?

Rain or Shine

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.

There's a Limit

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?

Golden Eggs

Age 16 to 18
Challenge Level

(1) You will need to know, or find out, the formula for the area of an ellipse. All you have to do then is solve a quadratic equation.

(2) What happens if you square this strange expression?