# Resources tagged with: Limits of Sequences

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There are 17 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 ### Litov's Mean Value Theorem

##### Age 11 to 14Challenge Level

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

##### Age 16 to 18Challenge 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? ### Slide

##### Age 16 to 18Challenge 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. ### Approximating Pi

##### Age 14 to 18Challenge 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? ### Climbing Powers

##### Age 16 to 18Challenge 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. . . . ### A Swiss Sum

##### Age 16 to 18Challenge Level

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

##### Age 14 to 18Challenge Level

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences? ### How Does Your Function Grow?

##### Age 16 to 18Challenge Level

Compares the size of functions f(n) for large values of n. ### Light Blue - Dark Blue

##### Age 7 to 11Challenge Level

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

##### Age 16 to 18Challenge 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? ### Small Steps

##### Age 16 to 18Challenge Level

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

##### Age 16 to 18

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

##### 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/...)). ### Continued Fractions I

##### Age 14 to 18

An article introducing continued fractions with some simple puzzles for the reader. ### Zooming in on the Squares

##### Age 7 to 14

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? ### Archimedes and Numerical Roots

##### Age 14 to 16Challenge 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? ### Little and Large

##### Age 16 to 18Challenge 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?