# Resources tagged with: Limits of Sequences

### There are 14 results

Broad Topics >

Patterns, Sequences and Structure > Limits of Sequences

##### 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.

##### 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?

##### 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.

##### Age 16 to 18

Challenge Level

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

##### Age 16 to 18

Challenge Level

$2\wedge 3\wedge 4$ could be $(2^3)^4$ or $2^{(3^4)}$. Does it make any difference? For both definitions, which is bigger: $r\wedge r\wedge r\wedge r\dots$ where the powers of $r$ go on for ever, or. . . .

##### 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?

##### Age 16 to 18

Challenge Level

A point moves around inside a rectangle. What are the least and the
greatest values of the sum of the squares of the distances from the
vertices?

##### Age 14 to 18

An article introducing continued fractions with some simple puzzles for the reader.

##### Age 16 to 18

In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).

##### Age 14 to 18

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?

##### Age 16 to 18

Challenge Level

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

##### Age 14 to 16

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?

##### Age 16 to 18

In this article we are going to look at infinite continued
fractions - continued fractions that do not terminate.

##### 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?