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Clickety Click and All the Sixes

Age 16 to 18 Challenge Level:

Why do this problem?

A non-standard problem based on place value and summing geometric series requiring simple manipulation of a numerical expression.

Possible approach

A short problem suitable as a lesson starter.

Key questions

Can you write the 10 digit number $6666666666$ as a geometric series?

Can you sum this series?

Can you do the same for any number that is a 'string of sixes'?

Possible extension

For a discussion of a generalisation of this problem see Sum The Series.