Continued Square Roots
The long ( infinitely
… ! ) row of complicatedlooking square root signs within this problem put it
firmly in the ‘Einstein cartoon ’ category, as far as Maths problems go, but
a bit of investigating will reveal pleasant surprises … The Problems : 1. Find the exact value
of the infinite sequence of square roots :
( If you have a
calculator with the previous ‘ANS’ button on it, then your working can be
repeated automatically by just pressing the ‘=’ button repeatedly once
you’ve figured out the sequence of steps you want to do ) 2. Repeat the problem
for :
You may be feeling
happier about these long sequences by now … 3. What about
? 4. Does
work out nicely ?
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