NRICH: Harmonic Triangle
Can you see how to build a harmonic triangle? Can you work out the next two rows?
This is the start of the harmonic triangle:
Each fraction is equal to the sum of the two fractions below it.
Look at the triangle above and check that the rule really does work.
Can you work out the next two rows?
The nth row starts with the fraction 1/n, so the first diagonal goes:
1/1, 1/2, 1/3, 1/4…
Take a look at the second diagonal:1/2, 1/6, 1/12, 1/20…
Can you see a pattern?
What fraction will appear in the second position on the nth row?
Can you prove it?
What about the third and fourth diagonals?
Age 14 to 16
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Resource k12
Can you see how to build a harmonic triangle? Can you work out the next two rows?
This is the start of the harmonic triangle:
Each fraction is equal to the sum of the two fractions below it.
Look at the triangle above and check that the rule really does work.
Can you work out the next two rows?
The nth row starts with the fraction 1/n, so the first diagonal goes:
1/1, 1/2, 1/3, 1/4…
Take a look at the second diagonal:1/2, 1/6, 1/12, 1/20…
Can you see a pattern?
What fraction will appear in the second position on the nth row?
Can you prove it?
What about the third and fourth diagonals?
Age 14 to 16
Click here for a poster of this problem.
What are you looking for?
Organization
Website URL
Type of Resource
PDF File