There are 18 NRICH Mathematical resources connected to Limits of sequences, you may find related items under Patterns, sequences and structure.
Broad Topics > Patterns, sequences and structure > Limits of sequences
Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
How much of the square is coloured blue? How will the pattern continue?
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.
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?
$2\wedge 3\wedge 4$ 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 $(r^r)^r$, where $r$ is $\sqrt{2}$?
Can you use the given image to say something about the sum of an infinite series?
Compares the size of functions f(n) for large values of n.
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.
In this article we are going to look at infinite continued fractions - continued fractions that do not terminate.
In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).
An article introducing continued fractions with some simple puzzles for the reader.
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?
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?
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?