Font (2 3) - + Letter spacing (4 5) - + Word spacing (6 7) - + Line spacing (8 9) - +

1.30 Examples of convergent and divergent sequences

Example (Newton’s approximation)

Let $a_{1}=1$ , then let

a_{n+1}={{1}\over{2}}\Bigl(a_{n}+{{2}\over{a_{n}}}\Bigr),

so the first few terms are as follows:

The sequence $1,0,1,0,1,0,\dots$ does not converge to anything.