Limits of sequences

problem
A swiss sum

Age

16 to 18

Challenge level

Can you use the given image to say something about the sum of an infinite series?
problem
Summing geometric progressions

Age

14 to 18

Challenge level

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
problem
Diminishing returns

Age

11 to 14

Challenge level

How much of the square is coloured blue? How will the pattern continue?
problem
How does your function grow?

Age

16 to 18

Challenge level

Compares the size of functions f(n) for large values of n.
problem
Litov's mean value theorem

Age

11 to 14

Challenge level

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
problem
Squareness

Age

16 to 18

Challenge level

The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?
problem
Slide

Age

16 to 18

Challenge level

This function involves absolute values. To find the slope on the slide use different equations to define the function in different parts of its domain.
problem
Light blue - dark blue

Age

7 to 11

Challenge level

Investigate the successive areas of light blue in these diagrams.
problem
Ruler

Age

16 to 18

Challenge level

The interval 0 - 1 is marked into halves, quarters, eighths ... etc. Vertical lines are drawn at these points, heights depending on positions. What happens as this process goes on indefinitely?
problem
Small steps

Age

16 to 18

Challenge level

Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.