problem

Favourite

### Summing geometric progressions

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

problem
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Summing geometric progressions

Favourite

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

problem
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Sixty-Seven Squared

Favourite

Evaluate these powers of 67. What do you notice? Can you convince
someone what the answer would be to (a million sixes followed by a
7) squared?

problem
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Clickety Click and all the Sixes

Favourite

What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6
where there are n sixes in the last term?

problem
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Magic Plant

Favourite

On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?

problem
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The Amazing Splitting Plant

Favourite

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

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Converging Product

Favourite

In the limit you get the sum of an infinite geometric series. What
about an infinite product (1+x)(1+x^2)(1+x^4)... ?

problem
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Circles ad infinitum

Favourite

A circle is inscribed in an equilateral triangle. Smaller circles
touch it and the sides of the triangle, the process continuing
indefinitely. What is the sum of the areas of all the circles?

problem
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Tower of Hanoi

Favourite

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.