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#### Resources tagged with Triangle numbers similar to Reciprocal Triangles:

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Broad Topics > Numbers and the Number System > Triangle numbers

### Reciprocal Triangles

##### Stage: 5 Challenge Level:

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

### Slick Summing

##### Stage: 4 Challenge Level:

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

### Speedy Summations

##### Stage: 5 Challenge Level:

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

### Mystic Rose

##### Stage: 4 Challenge Level:

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

### Iff

##### Stage: 4 Challenge Level:

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.

### Reasonable Algebra

##### Stage: 4 Challenge Level:

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

### Take Ten Sticks

##### Stage: 3 and 4 Challenge Level:

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?