Limits

There are 20 NRICH Mathematical resources connected to Limits

problem

Lower Bound

Age

14 to 16

Challenge level

What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =

problem

Witch of Agnesi

Age

16 to 18

Challenge level

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

problem

Reciprocal Triangles

Age

16 to 18

Challenge level

Prove that the sum of the reciprocals of the first n triangular numbers gets closer and closer to 2 as n grows.

problem

There's a limit

Age

14 to 18

Challenge level

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

Triangle Incircle Iteration

Age

14 to 16

Challenge level

Keep constructing triangles in the incircle of the previous triangle. What happens?

problem

Rain or Shine

Age

16 to 18

Challenge level

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.