I'm struggling on this but i get the feeling it's easier than i think.
The sequence is defined by:
xn+1 = (xn + 2) / 6
where the initial value is 0.
and you need to show that
| xn+1 - xn | </= (5/6) * |xn - xn+1 | </= (1/3) * (5/6)^n-1
after having shown that 0< xn <1 (which i was able to do).
( by the way </= means 'less that or equal to", i didn't know how to put it on the computer though.)
can anyone help?