# Plus Magazine

December 2005

## Series: solution

If you regularly deal with VAT, you'll have noticed that 17.5% = 10% + 5% + 2.5%. So you can easily calculate VAT by first taking 10%, then halving to get 5%, halving again to get 2.5%, and then adding up the three numbers. If the VAT rate were to increase in a way that sticks to this pattern, it would have to be increased by half of 2.5%, which is 1.25%. And if it gets increased again and again? Well, each time we halve the previous rate, so at the end of eternity the VAT rate will be

because the sum of the infinite geometric series in the brackets is 2.

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