Continued Square Roots
The long ( infinitely
… ! ) row of complicated-looking 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 ?
Open the File as a Word Document