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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

The second part of this question introduces an expression involving an infinite string of nested square roots but, as forbidding as it may seem, a little ingenuity is all that is needed to evaluate it.