Limits of sequences

There are 18 NRICH Mathematical resources connected to Limits of sequences
Little and Large
problem

Little and large

Age
16 to 18
Challenge level
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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?
Archimedes and numerical roots
problem

Archimedes and numerical roots

Age
14 to 16
Challenge level
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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?
Small Steps
problem

Small steps

Age
16 to 18
Challenge level
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Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.
Zooming in on the Squares
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Zooming in on the squares

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?
Continued Fractions I
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Continued fractions i

An article introducing continued fractions with some simple puzzles for the reader.
Continued Fractions II
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Continued fractions ii

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

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