Resources tagged with Limits of Sequences similar to Difference Dynamics:
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Working systematically. Iteration. Visualising. Networks/Graph Theory. Dynamical systems. Properties of numbers. Patterned numbers. Combinatorics. Limits of Sequences. Mathematical reasoning & proof.There are 7 results
Broad Topics > Sequences, Functions and Graphs > Limits of Sequences
Zooming in on the Squares
Stage: 2 and 3
Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
Happy Numbers
Stage: 3 Challenge Level: 
Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.
Summing Geometric Progressions
Stage: 4 and 5 Challenge Level:
Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
Approximating Pi
Stage: 4 and 5 Challenge Level:
By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?
Continued Fractions I
Stage: 4 and 5
An article introducing continued fractions with some simple puzzles for the reader.
Litov's Mean Value Theorem
Stage: 3 Challenge Level:
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Archimedes and Numerical Roots
Stage: 4 Challenge Level:
The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
NRICH is part of the family of activities in the Millennium Mathematics Project.