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'Sixty-seven Squared' printed from http://nrich.maths.org/
Why do this
An excellent exercise
in using geometric series with a fun way into the problem through
experimenting with numbers and making conjectures.
Let the students experiment with the numbers until they spot
patterns and make conjectures. If they don't see how to prove the
general result you may have to ask the 'key question' and suggest
using the sum of a geometric series.
Can you write the number (k sixes followed by a 7) in terms of
powers of 10 which will work for all k?
Try the problem
Clickety Click and All the Sixes