Limits of sequences

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

How much of the square is coloured blue? How will the pattern continue?

Compares the size of functions f(n) for large values of n.

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

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?

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.

Investigate the successive areas of light blue in these diagrams.

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?

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