You may also like
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?
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.
Copyright © 1997 - 2021. University of Cambridge.
All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.