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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.
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