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Resources tagged with Triangle numbers similar to Weekly Challenge 35: Clickety Click and All the Sixes:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > Numbers and the Number System > Triangle numbers

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Reciprocal Triangles

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Prove that the sum of the reciprocals of the first n triangular numbers gets closer and closer to 2 as n grows.

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Slick Summing

Stage: 4 Challenge Level: Challenge Level:1

Watch the video to see how Charlie works out the sum. Can you adapt his method?

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Speedy Summations

Stage: 5 Challenge Level: Challenge Level:1

Watch the video to see how to add together an arithmetic sequence of numbers efficiently.

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Route to Infinity

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you describe this route to infinity? Where will the arrows take you next?

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Iff

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Prove that if n is a triangular number then 8n+1 is a square number. Prove, conversely, that if 8n+1 is a square number then n is a triangular number.

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Reasonable Algebra

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use algebra to reason why 16 and 32 are impossible to create as the sum of consecutive numbers.

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Take Ten Sticks

Stage: 3 and 4 Challenge Level: Challenge Level:1

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?